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

被引：0
|
作者：
Ján Terpák
机构：
[1] Technical University of Kosice,Institute of Control and Informatization of Production Processes
来源：
Fractional Calculus and Applied Analysis | 2023年 / 26卷
关键词：
Fractional calculus (primary); Time-fractional diffusion-wave equation; Finite difference method; Grünwald-Letnikov derivative; MATLAB toolbox; 26A33 (primary); 35R11; 80M20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This 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.
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页码：599 / 618
页数：19
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