Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms
(2023) In Journal of Computational and Applied Mathematics 425.- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7cc80b0e-2eaa-45b9-a1ef-049001c5f14e
- author
- Engström, Christian LU ; Giani, Stefano and Grubišić, Luka
- publishing date
- 2023-06
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Fractional diffusion-wave equations, Numerical inverse Laplace transform, Numerical range, Resolvent estimates
- in
- Journal of Computational and Applied Mathematics
- volume
- 425
- article number
- 115035
- publisher
- Elsevier
- external identifiers
-
- scopus:85145347047
- ISSN
- 0377-0427
- DOI
- 10.1016/j.cam.2022.115035
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2022 The Author(s)
- id
- 7cc80b0e-2eaa-45b9-a1ef-049001c5f14e
- date added to LUP
- 2023-03-24 11:03:17
- date last changed
- 2023-03-24 13:21:46
@article{7cc80b0e-2eaa-45b9-a1ef-049001c5f14e,
abstract = {{<p>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.</p>}},
author = {{Engström, Christian and Giani, Stefano and Grubišić, Luka}},
issn = {{0377-0427}},
keywords = {{Fractional diffusion-wave equations; Numerical inverse Laplace transform; Numerical range; Resolvent estimates}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Journal of Computational and Applied Mathematics}},
title = {{Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms}},
url = {{http://dx.doi.org/10.1016/j.cam.2022.115035}},
doi = {{10.1016/j.cam.2022.115035}},
volume = {{425}},
year = {{2023}},
}