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Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms

Engström, Christian; Giani, Stefano; Grubišić, Luka

Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms Thumbnail


Authors

Christian Engström

Luka Grubišić



Abstract

In this paper, we consider the numerical inverse Laplace transform for distributed order time-fractional equations, where a discontinuous Galerkin scheme is used to discretize the problem in space. The success of Talbot’s approach for the computation of the inverse Laplace transform depends critically on the problem’s spectral properties and we present a method to numerically enclose the spectrum and compute resolvent estimates independent of the problem size. The new results are applied to time-fractional wave and diffusion-wave equations of distributed order.

Citation

Engström, C., Giani, S., & Grubišić, L. (2023). Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms. Journal of Computational and Applied Mathematics, 425, Article 115035. https://doi.org/10.1016/j.cam.2022.115035

Journal Article Type Article
Online Publication Date Dec 30, 2022
Publication Date 2023-06
Deposit Date Feb 27, 2023
Publicly Available Date Mar 28, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Electronic ISSN 1879-1778
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 425
Article Number 115035
DOI https://doi.org/10.1016/j.cam.2022.115035

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