Naslov
A spectral projection based method for the numerical solution of wave equations with memory

Autori
Engstrom, Christian ; Giani, Stefano ; Grubišić, Luka

Izvornik
Applied mathematics letters (0893-9659) 127 (2022); 107844, 9

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Inverse Laplace transform ; Spectral projection ; Wave equation with delay ; Finite element approximation

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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