Solutions of time-fractional diffusion equation with reflecting and absorbing boundary conditions using Matlab. (English) Zbl 1357.65207
Bélair, Jacques (ed.) et al., Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7–15, 2015. Cham: Springer (ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook). 15-25 (2016).
Summary: The main objective of this work is to develop Matlab programs for solving the time-fractional diffusion equation (TFDE) with reflecting and absorbing boundary conditions on finite and infinite domains. Essentially, there are three major codes, one for finding the exact solution of the TFDE and other two are for finding the numerical solution of the TFDE. The code for finding the exact solutions is based on the fundamental solution of the TFDE, whereas the codes for finding the numerical solutions are based on the explicit and the implicit finite difference schemes, respectively. Finally, we illustrate the effectiveness of the codes by applying them to TFDEs with sharp initial data and for various reflecting and absorbing boundary conditions both on finite and infinite domains. The results show the difference of solutions between the standard diffusion equation and the time-fractional diffusion equation.
For the entire collection see [Zbl 1362.00026].
For the entire collection see [Zbl 1362.00026].
MSC:
| 65M80 | Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R11 | Fractional partial differential equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65Y15 | Packaged methods for numerical algorithms |
Keywords:
numerical example; Matlab programs; time-fractional diffusion equation; reflecting and absorbing boundary conditions; fundamental solution; finite difference schemesSoftware:
MatlabReferences:
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