Portale Ricerca FVGhttps://ricerca.unityfvg.itThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 28 Jul 2021 00:25:13 GMT2021-07-28T00:25:13Z50521Computing the eigenvalues of Gurtin–MacCamy models with diffusionhttp://hdl.handle.net/11368/2562635Title: Computing the eigenvalues of Gurtin–MacCamy models with diffusion
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: Computing the eigenvalues of Gurtin–MacCamy models with diffusion
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11368/25626352012-01-01T00:00:00ZOn discretizing the semigroup of solution operators for linear time invariant - time delay systemshttp://hdl.handle.net/11368/2562691Title: On discretizing the semigroup of solution operators for linear time invariant - time delay systems
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: On discretizing the semigroup of solution operators for linear time invariant - time delay systems
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11368/25626912010-01-01T00:00:00ZThe interaction between charged macroions induced by rod-like ionshttp://hdl.handle.net/11368/2562688Title: The interaction between charged macroions induced by rod-like ions
Authors: Bohinc K.; Iglič A.; MASET, STEFANO; May S.
Description: The interaction between charged macroions induced by rod-like ions
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/25626882009-01-01T00:00:00ZEfficient computation of stability charts for linear time delay systemshttp://hdl.handle.net/11368/2562679Title: Efficient computation of stability charts for linear time delay systems
Authors: D. Breda; MASET, STEFANO; Vermiglio R.
Description: Efficient computation of stability charts for linear time delay systems
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11368/25626792005-01-01T00:00:00ZDiscretization of solution operators for linear time invariant - time delay systems in Hilbert spaceshttp://hdl.handle.net/11368/2562675Title: Discretization of solution operators for linear time invariant - time delay systems in Hilbert spaces
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: Discretization of solution operators for linear time invariant - time delay systems in Hilbert spaces
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11368/25626752012-01-01T00:00:00ZNumerical computation of characteristic multipliers for linear time periodic coefficients delay differential equationshttp://hdl.handle.net/11368/2562685Title: Numerical computation of characteristic multipliers for linear time periodic coefficients delay differential equations
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: Numerical computation of characteristic multipliers for linear time periodic coefficients delay differential equations
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11368/25626852006-01-01T00:00:00ZPseudospectral Techniques for Stability Computation of LinearTime Delay Systemshttp://hdl.handle.net/11368/2562681Title: Pseudospectral Techniques for Stability Computation of LinearTime Delay Systems
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: Pseudospectral Techniques for Stability Computation of LinearTime Delay Systems
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11368/25626812005-01-01T00:00:00ZDebye–Hückel theory for mixtures of rigid rodlike ions and salthttp://hdl.handle.net/11368/2562661Title: Debye–Hückel theory for mixtures of rigid rodlike ions and salt
Authors: Bohinc K.; Reščič J.; MASET, STEFANO; May S.
Description: Debye–Hückel theory for mixtures of rigid rodlike ions and salt
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11368/25626612011-01-01T00:00:00ZNumerical recipes for investigating endemic equilibria of age-structured SIR epidemicshttp://hdl.handle.net/11368/2562658Title: Numerical recipes for investigating endemic equilibria of age-structured SIR epidemics
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: The subject of this paper is the analysis of the equibria of a SIR
type epidemic model, which is taken as a case study among the wide family
of dynamical systems of infinite dimension. For this class of systems both
the determination of the stationary solutions and the analysis of their local
asymptotic stability are often unattainable theoretically, thus requiring the
application of existing numerical tools and/or the development of new ones.
Therefore, rather than devoting our attention to the SIR model’s features, its
biological and physical interpretation or its theoretical mathematical analysis,
the main purpose here is to discuss how to study its equilibria numerically, es-
pecially as far as their stability is concerned. To this end, we briefly analyze the
construction and solution of the system of nonlinear algebraic equations lead-
ing to the stationary solutions, and then concentrate on two numerical recipes
for approximating the stability determining values known as the characteristic
roots. An algorithm for the purpose is given in full detail. Two applications
are presented and discussed in order to show the kind of results that can be
obtained with these tools.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11368/25626582012-01-01T00:00:00ZAPPROXIMATION OF EIGENVALUES OF EVOLUTIONOPERATORS FOR LINEAR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONShttp://hdl.handle.net/11368/2562660Title: APPROXIMATION OF EIGENVALUES OF EVOLUTIONOPERATORS FOR LINEAR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: This paper deals with the approximation of the eigenvalues of evolution operators for
linear retarded functional differential equations through the reduction to finite dimensional operators
by a pseudospectral collocation. Fundamental applications such as determination of asymptotic
stability of equilibria and periodic solutions of nonlinear autonomous retarded functional differential
equations follow at once. Numerical tests are provided.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11368/25626602012-01-01T00:00:00ZAttraction between negatively charged surfaces mediated by spherical counterions with quadrupolar charge distributionhttp://hdl.handle.net/11368/2562668Title: Attraction between negatively charged surfaces mediated by spherical counterions with quadrupolar charge distribution
Authors: Urbanija J.; Bohinc K.; BELLEN, ALFREDO; MASET, STEFANO; Iglič A.; Kralj Iglič V.; P. B. Sunil Kumar
Description: Attraction between negatively charged surfaces mediated by spherical counterions with quadrupolar charge distribution
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11368/25626682008-01-01T00:00:00ZAn adaptive algorithm for efficient computation of level curves of surfaceshttp://hdl.handle.net/11368/2562664Title: An adaptive algorithm for efficient computation of level curves of surfaces
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: An adaptive algorithm for efficient computation of level curves of surfaces
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/25626642009-01-01T00:00:00ZStability analysis of age-structured population
equations by pseudospectral differencing methodshttp://hdl.handle.net/11368/2635331Title: Stability analysis of age-structured population
equations by pseudospectral differencing methods
Authors: Breda D.; Cusulin C.; Iannelli M.; MASET, STEFANO; Vermiglio R.
Description: In this paper a numerical scheme to investigate the stability of linear models of age-structured population dynamics is studied. The method is based on the discretization of the infinitesimal generator associated to the semigroup of the solution operator by using pseudospectral differencing techniques, hence following the approach recently proposed in Breda et al. [SIAM J Sci Comput
27(2): 482–495, 2005] for delay differential equations. The method computes the rightmost characteristic roots and it is shown to converge with spectral accuracy behavior.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11368/26353312007-01-01T00:00:00ZPseudospectral approximation of eigenvalues of derivative
operators with non-local boundary conditionshttp://hdl.handle.net/11368/2635332Title: Pseudospectral approximation of eigenvalues of derivative
operators with non-local boundary conditions
Authors: Breda D.; MASET, STEFANO; Vermiglio R.
Description: By taking as a “prototype problem” a one-delay linear autonomous system of delay differential equations we
present the problem of computing the characteristic roots of a retarded functional differential equation as an
eigenvalue problem for a derivative operator with non-local boundary conditions given by the particular system
considered. This theory can be enlarged to more general classes of functional equations such as neutral delay
equations, age-structured population models and mixed-type functional differential equations.
It is thus relevant to have a numerical technique to approximate the eigenvalues of derivative operators under nonlocal
boundary conditions. In this paper we propose to discretize such operators by pseudospectral techniques and
turn the original eigenvalue problem into a matrix eigenvalue problem. This approach is shown to be particularly
efficient due to the well-known “spectral accuracy” convergence of pseudospectral methods. Numerical examples
are given.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11368/26353322006-01-01T00:00:00ZStability analysis of the Gurtin-MacCamy modelhttp://hdl.handle.net/11368/2634396Title: Stability analysis of the Gurtin-MacCamy model
Authors: Breda D.; Iannelli M.; MASET, STEFANO; Vermiglio R.
Description: In this paper we propose a numerical scheme to investigate the stability of steady
states of the nonlinear Gurtin–MacCamy system, which is a basic model in population dynamics.
In fact the analysis of stability is usually performed by the study of transcendental characteristic
equations that are too difficult to approach by analytical methods. The method is based on the
discretization of the infinitesimal generator associated to the semigroup of the solution operator by
using pseudospectral differencing techniques. The method computes the rightmost characteristic
roots, and it is shown to converge with spectral accuracy behavior.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11368/26343962008-01-01T00:00:00ZStability properties of explicit exponential Runge–Kutta methodshttp://hdl.handle.net/11368/2634192Title: Stability properties of explicit exponential Runge–Kutta methods
Authors: MASET, STEFANO; ZENNARO, MARINO
Description: In this paper we study conditional stability properties of exponential Runge–Kutta methods when they
are applied to semilinear systems of ordinary differential equations characterized by a stiff linear part and
a nonstiff nonlinear part. In particular,we obtain sufficient conditions under which an explicit method
satisfies such conditional properties. We also study the unconditional stability properties introduced in
our previous paper (Maset & Zennaro,2008,Unconditional stability of explicit exponential Runge-Kutta
methods for semi-linear ordinary differential equations. Math. Comput.,78,957–967). In particular,we
obtain a necessary condition for such unconditional properties. By using the sufficient conditions for the
conditional properties and the necessary condition for the unconditional properties,we analyse and classify
the most popular explicit methods. The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11368/26341922013-01-01T00:00:00ZTRACE-DDE: A Tool for Robust Analysis and Characteristic Equations for Delay Differential Equationshttp://hdl.handle.net/11368/2985Title: TRACE-DDE: A Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations
Authors: BREDA D; MASET, STEFANO; VERMIGLIO R.
Description: TRACE-DDE: A Tool for Robust Analysis and Characteristic Equations for Delay Differential Equations
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/29852009-01-01T00:00:00ZTime transformation for delay differential equationshttp://hdl.handle.net/11368/3288Title: Time transformation for delay differential equations
Authors: Brunner H.; MASET, STEFANO
Description: We study changes of variable, called time transformations, which
reduce a delay differential equation (DDE) with a variable non-vanishing delay
and an unbounded lag function to another DDE with a constant delay. By
using this reduction, we can easily obtain a superconvergent integration of the
original equation, even in the case of a non-strictly-increasing lag function, and
study the type of decay to zero of solutions of scalar linear non-autonomous
equations with a strictly increasing lag function.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/32882009-01-01T00:00:00ZPseudospectral methods for stability analysis of delayed dynamical systemshttp://hdl.handle.net/11368/2769327Title: Pseudospectral methods for stability analysis of delayed dynamical systems
Authors: D. Breda; MASET, STEFANO; R. Vermiglio
Description: In order to investigate the stability of both equilibria
and periodic orbits of linear delayed dynamical systems
we employ the numericalmethod recently proposed by
the authors for discretizing the associated evolution family.
The objective is the efficient computation of stability charts
for varying or uncertain system parameters. A benchmark
set of tests is provided including computational data such as
the accuracy of the stability boundaries and the total computational
time, with particular reference to the delayed Mathieu
equation.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11368/27693272014-01-01T00:00:00ZAn asymptotic theorem for substitution-resistant authentication codeshttp://hdl.handle.net/11368/2309874Title: An asymptotic theorem for substitution-resistant authentication codes
Authors: MASET, STEFANO; SGARRO, ANDREA
Description: ...
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11368/23098741993-01-01T00:00:00ZAsymptotic stability in the numerical solution of linear pure delay differential equations as abstract Cauchy problems. J. Comput. Appl. Math. 111 (1999), no. 1-2, 163--172. 65L20 (34A45 34K05)http://hdl.handle.net/11368/1697488Title: Asymptotic stability in the numerical solution of linear pure delay differential equations as abstract Cauchy problems. J. Comput. Appl. Math. 111 (1999), no. 1-2, 163--172. 65L20 (34A45 34K05)
Authors: MASET, STEFANO
Description: Asymptotic stability in the numerical solution of linear pure delay differential equations as abstract Cauchy problems.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11368/16974881999-01-01T00:00:00ZStability of Runge-Kutta methods for linear delay differential equations.http://hdl.handle.net/11368/1697486Title: Stability of Runge-Kutta methods for linear delay differential equations.
Authors: MASET, STEFANO
Description: This paper investigates the stability of Runge.Kutta methods when they are applied to the complex linear scalar delay differential equations.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11368/16974862000-01-01T00:00:00ZPseudospectral differencing methods for characteristic roots of delay differential equationshttp://hdl.handle.net/11368/1697478Title: Pseudospectral differencing methods for characteristic roots of delay differential equations
Authors: D. BREDA; MASET, STEFANO; R. VERMIGLIO
Description: In [D. Breda, S. Maset, and R. Vermiglio, IMA J. Numer. Anal., 24 (2004), pp. 1– 19.] and [D. Breda, The Infinitesimal Generator Approach for the Computation of Characteristic Roots for Delay Differential Equations Using BDF Methods, Research report UDMI RR17/2002, Dipartimento di Matematica e Informatica, Universit`a degli Studi di Udine, Udine, Italy, 2002.] the authors proposed to compute the characteristic roots of delay differential equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge–Kutta (RK) and linear multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based on pseudospectral differencing techniques. We prove the “spectral accuracy” convergence behavior typical of pseudospectral schemes, as also illustrated by some numerical experiments.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11368/16974782006-01-01T00:00:00ZRunge-Kutta Methods for Retarded Functional Differential Equationshttp://hdl.handle.net/11368/1697476Title: Runge-Kutta Methods for Retarded Functional Differential Equations
Authors: MASET, STEFANO; TORELLI, LUCIO; R. VERMIGLIO
Description: We introduce Runge–Kutta (RK) methods for Retarded Functional Differential Equations
(RFDEs).With respect to RK methods (A, b, c) for Ordinary Differential Equations
the weights vector b ∈ Rs and the coefficients matrix A ∈ Rs×s are replaced by Rsvalued
and Rs×s-valued polynomial functions b(·) and A(·) respectively. Such methods
for RFDEs are different from Continuous RK (CRK) methods where only the weights
vector is replaced by a polynomial function. We develop order conditions and construct
explicit methods up to the convergence order four.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11368/16974762005-01-01T00:00:00ZComputing the characteristic roots for delay differential equationshttp://hdl.handle.net/11368/1697477Title: Computing the characteristic roots for delay differential equations
Authors: D. BREDA; MASET, STEFANO; R. VERMIGLIO
Description: A new approach to computing the rightmost characteristic roots of linear Delay DifferentialEquations (DDEs) with multiple discrete and distributed delays is presented. It is based onthe discretization of the infinitesimal generator of the solution operators semigroup andit avoids the use of the characteristic equation. The approximated roots are obtained by alarge sparse standard eigenvalue problem.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/11368/16974772004-01-01T00:00:00ZA multigrid method of the second kind for solving linear systems of ODEs discretized by continuous Runge-Kutta methods.http://hdl.handle.net/11368/1697484Title: A multigrid method of the second kind for solving linear systems of ODEs discretized by continuous Runge-Kutta methods.
Authors: MASET, STEFANO
Description: A multigrid method of the second kind for solving linear systems of ODEs discretized by continuous Runge-Kutta methods.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/11368/16974842002-01-01T00:00:00ZOrientations of dipoles restricted by two oppositely charged wallshttp://hdl.handle.net/11368/1697480Title: Orientations of dipoles restricted by two oppositely charged walls
Authors: BOHINC K; MASET, STEFANO
Description: Orientations of dipoles restricted by two oppositely charged walls
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11368/16974802007-01-01T00:00:00ZInstability of Runge-Kutta methods when applied to linear systems of delay differential equationshttp://hdl.handle.net/11368/1697485Title: Instability of Runge-Kutta methods when applied to linear systems of delay differential equations
Authors: MASET, STEFANO
Description: Instability of Runge-Kutta methods when applied to linear systems of delay differential equations
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/11368/16974852002-01-01T00:00:00ZNumerical Solution of Retarded Functional Differential Equations as Abstract Cauchy problemshttp://hdl.handle.net/11368/1697479Title: Numerical Solution of Retarded Functional Differential Equations as Abstract Cauchy problems
Authors: MASET, STEFANO
Description: Numerical Solution of Retarded Functional Differential Equations as Abstract Cauchy problems
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11368/16974792003-01-01T00:00:00ZNumerical solution of constant coefficient linear delay differential equations as abstract Cauchy problemshttp://hdl.handle.net/11368/1690033Title: Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems
Authors: BELLEN, ALFREDO; MASET, STEFANO
Description: In this paper we present an approach, for the numerical solution of linear delay differential equations, different from the classical step-by-step method. We restate the equation as an abstract Cauchy problem and then we discretize it in a system of ordinary differential equations. The scheme of discretization is proved to be convergent. Moreover the asymptotic stability is investigated for two significan classes of asymptotically stable problems.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11368/16900332000-01-01T00:00:00ZNumerical methods for delay models in biomathematicshttp://hdl.handle.net/11368/1687916Title: Numerical methods for delay models in biomathematics
Authors: BELLEN, ALFREDO; GUGLIELMI N; MASET, STEFANO
Description: Two different approaches for the numerical approximation of delay differential equations describing here the time evolution of biological systems are discussed. One of the numerical approaches is mainly designed to solve stiff problems and the other to solve non-stiff problems. Numerical codes are also referred to. One of the main goals of the authors is also to emphasize the main difficulties arising in the numerical integration of such delay differential equations compared to those based on ODEs. The method is applied to the Waltman model on antibody production based on equations with state-dependent-delays.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11368/16879162006-01-01T00:00:00ZSuperconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays.http://hdl.handle.net/11368/1690038Title: Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays.
Authors: BELLEN, ALFREDO; BRUNNER H; MASET, STEFANO; TORELLI, LUCIO
Description: We study the optimal order of (global and local) superconvergence of piecewise polynomial collocation on quasi-graded meshes for functional differential equations with (nonlinear) delays vanishing at t=0. It is shown that while for linear delays (e.g. proportional delays qt with 0<q<1) and certain nonlinear delays the classical order results still hold, high degree of tangency with the identity function at t=0 leads not only to a reduction in the order of superconvergence but also to very serious difficulties in the actual computation of numerical approximations.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11368/16900382006-01-01T00:00:00ZContractive initializing methods for the pantograph equation of neutral typehttp://hdl.handle.net/11368/1702088Title: Contractive initializing methods for the pantograph equation of neutral type
Authors: BELLEN A; MASET, STEFANO; TORELLI, LUCIO
Description: Contractive initializing methods for the pantograph equation of neutral type
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/11368/17020882001-01-01T00:00:00ZUnconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equationshttp://hdl.handle.net/11368/1934801Title: Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations
Authors: MASET, STEFANO; ZENNARO, MARINO
Description: In this paper we define unconditional stability properties of exponential Runge-Kutta methods when they are applied to semi-linear systems of ordinary differential equations characterized by a stiff linear part and a nonstiff non-linear part. These properties are related to a class of systems and to a specific norm. We give sufficient conditions in order that an explicit method satisfies such properties. On the basis of such conditions we analyze some of the popular methods.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/19348012009-01-01T00:00:00ZNumerical approximation of characteristic values of Partial Retarded Functional Differential Equationshttp://hdl.handle.net/11368/1918805Title: Numerical approximation of characteristic values of Partial Retarded Functional Differential Equations
Authors: BREDA D.; MASET, STEFANO; VERMIGLIO R.
Description: The stability of an equilibrium point of a dynamical system is determinedby the position in the complex plane of the so-called characteristic values of the linearizationaround the equilibrium. This paper presents an approach for the computationof characteristic values of partial differential equations of evolution involving timedelay, which is based on a pseudospectral method coupled with a spectral method.The convergence of the computed characteristic values is of infinite order with respectto the pseudospectral discretization and of finite order with respect to the spectralone. However, for one dimensional reaction diffusion equations, the finite order of thespectral discretization is proved to be so high that the convergence turns out to be asfast as one of infinite order.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/19188052009-01-01T00:00:00ZBridging like-charged macroions through longdivalent rod-like ionshttp://hdl.handle.net/11368/1918814Title: Bridging like-charged macroions through longdivalent rod-like ions
Authors: MAY S; IGLIC A; RESCIC J; MASET, STEFANO; BOHINC K.
Description: Bridging like-charged macroions through longdivalent rod-like ions
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11368/19188142008-01-01T00:00:00ZAttraction between like-charged surfaces induced byorientational ordering of divalent rigid rod-likecounterions: theory and simulationshttp://hdl.handle.net/11368/1918780Title: Attraction between like-charged surfaces induced byorientational ordering of divalent rigid rod-likecounterions: theory and simulations
Authors: MASET, STEFANO; RESCIC J; BOHINC K.
Description: Attraction between like-charged surfaces induced by orientational ordering of divalent rigid
rod-like counterions: theory and simulations.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/19187802009-01-01T00:00:00ZRecent trends in the numerical solution of retarded functional differential equationshttp://hdl.handle.net/11368/2262189Title: Recent trends in the numerical solution of retarded functional differential equations
Authors: BELLEN, ALFREDO; GUGLIELMI N.; MASET, STEFANO; ZENNARO, MARINO
Description: Retarded functional differential equations (RFDEs) form a wide class of evolution equations which share the property that, at any point, the rate of the solution depends on a discrete or distributed set of values attained by the solution itself in the past. Thus the initial problem for RFDEs is an infinitedimensional problem, taking its theoretical and numerical analysis beyond the classical schemes developed for differential equations with no functional elements. In particular, numerically solving initial problems for RFDEs is a difficult task that cannot be founded on the mere adaptation of well-known methods for ordinary, partial or integro-differential equations to the presence of retarded arguments. Indeed, efficient codes for their numerical integration need specific approaches designed according to the nature of the equation and the behaviour of the solution.
By defining the numerical method as a suitable approximation of the solution map of the given equation, we present an original and unifying theory for the convergence and accuracy analysis of the approximate solution. Two particular approaches, both inspired by Runge–Kutta methods, are described. Despite being apparently similar, they are intrinsically different. Indeed, in the presence of specific types of functionals on the right-hand side, only one of them can have an explicit character, whereas the other gives rise to an overall procedure which is implicit in any case, even for non-stiff problems.
In the panorama of numerical RFDEs, some critical situations have been recently investigated in connection to specific classes of equations, such as the accurate location of discontinuity points, the termination and bifurcation of the solutions of neutral equations, with state-dependent delays, the regularization of the equation and the generalization of the solution behind possible termination points, and the treatment of equations stated in the implicit form, which include singularly perturbed problems and delay differential-algebraic equations as well. All these issues are tackled in the last three sections.
In this paper we have not considered the important issue of stability, for which we refer the interested reader to the comprehensive book by Bellen and Zennaro (2003).
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/22621892009-01-01T00:00:00ZTime transformation for state-dependent delay differential equationshttp://hdl.handle.net/11368/2309875Title: Time transformation for state-dependent delay differential equations
Authors: BRUNNER H.; MASET, STEFANO
Description: We study changes of variable, called time transformations, which
reduce a delay differential equation (DDE) with a variable non-vanishing delay
and an unbounded lag function to another DDE with a constant delay. By
using this reduction, we can easily obtain a superconvergent integration of the
original equation, even in the case of a non-strictly-increasing lag function, and
study the type of decay to zero of solutions of scalar linear non-autonomous
equations with a strictly increasing lag function.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11368/23098752010-01-01T00:00:00ZComputation of asymptotic stability for a class of partial differential equations with delay.http://hdl.handle.net/11368/2309876Title: Computation of asymptotic stability for a class of partial differential equations with delay.
Authors: BREDA D.; MASET, STEFANO; VERMIGLIO R.
Description: Computation of asymptotic stability for a class of partial differential equations with delay.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11368/23098762010-01-01T00:00:00ZAnalysis of Numerical Integration for Time Delay Systemshttp://hdl.handle.net/11368/2296520Title: Analysis of Numerical Integration for Time Delay Systems
Authors: BELLEN, ALFREDO; MASET, STEFANO
Description: The paper provides an original presentation ofthe numerical integration of General Retarded Functional Differential Equations as a sequence of approximations of the states of the system. The global error analysis is developed for one-step methods and order conditions are provided for a suitable generalization of explicit Runge-Kutta methods
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11368/22965202009-01-01T00:00:00ZThe Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating Argumentshttp://hdl.handle.net/11368/2855425Title: The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating Arguments
Authors: MASET, STEFANO
Description: We consider the numerical solution of boundary value problems for neutral differential equations with deviating arguments by the collocation method, which includes the finite element method and the spectral element method. By using the results of Part I [SIAM J. Numer. Anal., 53 (2015), pp. 2771--2793] of this paper, we obtain concrete convergence theorems for this particular type of functional differential equations.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11368/28554252015-01-01T00:00:00ZA numerical approach for investigating the stability of equilibria for structured population modelshttp://hdl.handle.net/11368/2769326Title: A numerical approach for investigating the stability of equilibria for structured population models
Authors: D. Breda; O. Diekmann; MASET, STEFANO; R. Vermiglio
Description: We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer–resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11368/27693262013-01-01T00:00:00ZGood behaviour with respect to the stiffness in the numerical integration of retarded functional differential equationshttp://hdl.handle.net/11368/2805928Title: Good behaviour with respect to the stiffness in the numerical integration of retarded functional differential equations
Authors: MASET, STEFANO; ZENNARO, MARINO
Description: In this paper we obtain, for the global errors of a functional continuous Runge–Kutta (FCRK) method as applied to a retarded functional differential equation (RFDE), a recursive relation similar to that obtained for the global errors of a one-step method as applied to an ordinary differential equation. After which, we introduce a notion of good behavior with respect to the stiffness of an FCRK method on a given family of RFDEs. Finally, we analyze this notion of “good behavior” in the case of particular families of scalar semilinear RFDEs with nonvanishing delays.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11368/28059282014-01-01T00:00:00ZInteraction between Charged Cylinders in Electrolyte Solution; Excluded Volume Effecthttp://hdl.handle.net/11368/2915304Title: Interaction between Charged Cylinders in Electrolyte Solution; Excluded Volume Effect
Authors: Huang, Beibei; Maset, Stefano; Bohinc, Klemen
Description: Electrostatic interactions govern the physical properties of charged cylindrical structures in electrolyte solutions. Besides the surface charge on the cylinders, another factor influencing the electrostatic interactions are the mobile ions. The finite size of the mobile ions is included by the excluded volume effect within the lattice statistics, while the electrostatic interactions are considered by means of the mean electrostatic field. In this article we consider charged parallel cylinders embedded into an electrolyte solution of mobile monovalent ions. A modified nonlinear Poisson-Boltzmann equation is proposed via variational procedure, and we implement the finite element method to solve it numerically. Excluded volume effect of the system containing two and multiple charged parallel cylinders are taken into account. Numerical results show that the excluded volume effect decreases the concentration of counterion and increases the electrostatic potential near the charged cylinders. The angular distribution of counterion around the particular cylinder is asymmetric. The study of the electrostatic interaction between two parallel equally charged cylinders reveals that an increase in the free energy is seen when the ionic strength is decreased. The free energy decreases as a function of the cylinders separation distance. On the contrary for two oppositely charged cylinders, the free energy increases with increasing cylinder separation distance, while for two cylinders with different charged density it shows nonmonotonic variation with the increasing cylinders separation distance. (Graph Presented).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11368/29153042017-01-01T00:00:00ZInteraction between like-charged surfaces mediated by uniformly charged counter-nanoparticleshttp://hdl.handle.net/11368/2943665Title: Interaction between like-charged surfaces mediated by uniformly charged counter-nanoparticles
Authors: Spada, Simone; Maset, Stefano; Bohinc, Klemen
Description: An electric interfacial layer appears when the mobile ions or nanoparticles of an electrolyte solution interact with an extended, charged surface. The distribution of ions or nanoparticles is driven by electrostatic interactions and entropy. We consider continuously charged spherical nanoparticles of finite size. At thermodynamic equilibrium, the spatial profile of the concentration is obtained by deriving the appropriate Euler-Lagrange equations. We discuss how various model parameters of the nanoparticles influence structural properties of the electric interfacial layer. We calculate the pressure between two like-charged surfaces embedded in a water solution of continuously charged spherical nanoparticles.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11368/29436652019-01-01T00:00:00ZTime-transformations for the event location in discontinuous ODEshttp://hdl.handle.net/11368/2929621Title: Time-transformations for the event location in discontinuous ODEs
Authors: Lopez, L.; Maset, S.
Description: In this paper, we consider numerical methods for the location of
events of ordinary differential equations. These methods are based on particular
changes of the independent variable, called time-transformations. Such a
time-transformation reduces the integration of an equation up to the unknown
point, where an event occurs, to the integration of another equation up to a
known point. This known point corresponds to the unknown point by means
of the time-transformation. This approach extends the one proposed by Dieci
and Lopez [BIT 55 (2015), no. 4, 987–1003], but our generalization permits,
amongst other things, to deal with situations where the solution approaches
the event in a tangential way. Moreover, we also propose to use this approach
in a different manner with respect to that of Dieci and Lopez.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11368/29296212018-01-01T00:00:00ZInfluence of added salt on the surface induced ordering of nanoparticles with discretely distributed chargeshttp://hdl.handle.net/11368/2955704Title: Influence of added salt on the surface induced ordering of nanoparticles with discretely distributed charges
Authors: Bohinc K.; Rescic J.; Spada S.; May S.; Maset S.
Description: The formation of an electric double layer composed of spherical nanoparticles is analyzed by means of a generalized Poisson-Boltzmann model and Monte Carlo simulations. We study a solution of symmetric and asymmetric mixtures of spherical particles that reside between two planar like-charged surfaces. Each spherical particle carries two elementary charges that are attached at its poles. The electrolyte solution also contains monovalent point-like salt ions. Our theoretical model properly accounts for intra-particle correlations - that is correlations between the spatially separated charges belonging to a single multivalent spherical particle. Correlations between different spherical particles are neglected. It is shown that added salt decreases the number density close to the charged surface and influences the orientation of spherical particles. Increasing salt concentration decreases the order parameter of the spherical particles. Generalized Poisson-Boltzmann results, obtained by solving an integral differential equation, and predictions from Monte Carlo (MC) simulations are in excellent agreement.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11368/29557042019-01-01T00:00:00ZStability of Linear Delay Differential Equations. A Numerical Approach with MATLABhttp://hdl.handle.net/11368/2847070Title: Stability of Linear Delay Differential Equations. A Numerical Approach with MATLAB
Authors: Breda, Dimitri; MASET, STEFANO; Vermiglio, Rossana
Description: This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11368/28470702015-01-01T00:00:00ZThe Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Resultshttp://hdl.handle.net/11368/2855423Title: The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results
Authors: MASET, STEFANO
Description: We consider the numerical solution of boundary value problems for general neutral functional differential equations by the collocation method. The collocation method can be applied in two versions: the finite element method and the spectral element method. We give convergence results for the collocation method deduced by the convergence theory developed in [S. Maset, Numer. Math., (2015), pp. 1--31] for a general discretization of an abstract reformulation of the problems. Such convergence results are then applied in Part II [S. Maset, SIAM J. Numer. Anal., 53 (2015), pp. 2794--2821] of this paper to boundary values problems for a particular type of neutral functional differential equations, namely, differential equations with deviating arguments.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11368/28554232015-01-01T00:00:00Z