Author
Stefano Maset
Bio: Stefano Maset is an academic researcher from University of Trieste. The author has contributed to research in topics: Delay differential equation & Differential equation. The author has an hindex of 19, co-authored 58 publications receiving 1295 citations.
Papers published on a yearly basis
Papers
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TL;DR: The proposed approach 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 is proposed.
Abstract: 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, Universita 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.
259 citations
TL;DR: A new approach to computing the rightmost characteristic roots of linear Delay Differential Equations (DDEs) with multiple discrete and distributed delays is presented, based on the discretization of the infinitesimal generator of the solution operators semigroup.
Abstract: A new approach to computing the rightmost characteristic roots of linear Delay Differential Equations (DDEs) with multiple discrete and distributed delays is presented. It is based on the discretization of the infinitesimal generator of the solution operators semigroup and it avoids the use of the characteristic equation. The approximated roots are obtained by a large sparse standard eigenvalue problem.
112 citations
TL;DR: This paper proposes to discretize derivative operators by pseudospectral techniques and turn the original eigenvalue problem into a matrix eigen value problem, which is shown to be particularly efficient due to the well-known "spectral accuracy" convergence of pseudOSpectral methods.
106 citations
Book•
21 Oct 2014
TL;DR: The local dynamics of a parabolic germ was studied in this article, and the results showed that the dynamics of the parabolic germs can be represented by a global theory of global theory.
Abstract: 1 Introduction.- 2 Local dynamics of a parabolic germ.- 3 Global theory.- 4 Numerical results.- 5 For dessert: several amusing examples.- Index.
104 citations
TL;DR: In this paper, the authors present a Matlab package TRACE-DDE devoted to the computation of characteristic roots and stability charts of linear autonomous systems of delay differential equations with discrete and distributed delays and resume the main features of the underlying pseudospectral approach.
Abstract: In the recent years the authors developed numerical schemes to detect the stability properties of different classes of systems involving delayed terms. The base of all methods is the use of pseudospectral differentiation techniques in order to get numerical approximations of the relevant characteristic eigenvalues. This chapter is aimed to present the freely available Matlab package TRACE-DDE devoted to the computation of characteristic roots and stability charts of linear autonomous systems of delay differential equations with discrete and distributed delays and to resume the main features of the underlying pseudospectral approach.
79 citations
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2,084 citations
01 Mar 1987
TL;DR: The variable-order Adams method (SIVA/DIVA) package as discussed by the authors is a collection of subroutines for solution of non-stiff ODEs.
Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
1,955 citations
TL;DR: In this paper, the authors present a panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis.
Abstract: Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis.
569 citations