General one-dimensional model of the time-fractional diffusion-wave equation in various geometries-Reference-Cited by-同舟云学术

General one-dimensional model of the time-fractional diffusion-wave equation in various geometries

Published:2023-03-20 Issue:2 Volume:26 Page:599-618
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:Fract Calc Appl Anal

Author:

Terpák Ján^ORCID

Abstract

AbstractThis paper deals with the analysis of the time-fractional diffusion-wave equation as one-dimensional problem in a large plane wall, long cylinder, and sphere. The result of the analysis is the proposal of one general mathematical model that describes various geometries and different processes. Finite difference method for solving the time-fractional diffusion-wave equation using Grünwald-Letnikov definition for homogeneous or inhomogeneous material and for homogeneous or inhomogeneous boundary conditions is described. Dirichlet, Neumann and Robin boundary conditions are considered. Implementation of numerical methods for explicit, implicit, and Crank-Nicolson scheme were realised in MATLAB. Finally, illustrative examples of simulations using the developed toolbox are presented.

Funder

Agentúra na Podporu Výskumu a Vývoja

Vedecká Grantová Agentúra MšVVaš SR a SAV

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s13540-023-00138-3.pdf

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