Numerical approximation of characteristic values of partial retarded functional differential equations |
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Authors: | D Breda S Maset R Vermiglio |
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Institution: | (1) Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italy;(2) Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Via Valerio 12, 34127 Trieste, Italy |
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Abstract: | The stability of an equilibrium point of a dynamical system is determined by the position in the complex plane of the so-called
characteristic values of the linearization around the equilibrium. This paper presents an approach for the computation of
characteristic values of partial differential equations of evolution involving time delay, which is based on a pseudospectral
method coupled with a spectral method. The convergence of the computed characteristic values is of infinite order with respect
to the pseudospectral discretization and of finite order with respect to the spectral one. However, for one dimensional reaction
diffusion equations, the finite order of the spectral discretization is proved to be so high that the convergence turns out
to be as fast as one of infinite order. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 65N25 65N35 34K30 35R10 47D06 |
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