Paper Info
Title
A spectral projection based method for the numerical solution of wave equations with memory
Abstract
In this paper, we compare two approaches to numerically approximate the solution of second-order Gurtin-Pipkin type of integro-differential equations. Both methods are based on a high-order Discontinous Galerkin approximation in space and the numerical inverse Laplace transform. In the first approach, we use functional calculus and the inverse Laplace transform to represent the solution. The spectral projections are then numerically computed and the approximation of the solution of the time-dependent problem is given by a summation of terms that are the product of projections of the data and the inverse Laplace transform of scalar functions. The second approach is the standard inverse Laplace transform technique. We show that the approach based on spectral projections can be very efficient when several time points are computed, and it is particularly interesting for parameter-dependent problems where the data or the kernel depends on a parameter. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Year
DOI
Venue
2022
10.1016/j.aml.2021.107844
APPLIED MATHEMATICS LETTERS
Keywords
DocType
Volume
Inverse Laplace transform, Spectral projection, Wave equation with delay, Finite element approximation
Journal
127
ISSN
Citations 
PageRank 
0893-9659
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Christian Engström1134.97
Stefano Giani200.68
Luka Grubisic300.34