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

Engström, Christian; Giani, Stefano; Grubišić, Luka

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: Feb 27, 2023
• 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