The Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation
| Autor: | Chuanzeng Zhang, Zhi-Zhong Yan, Cheng-Feng Zheng |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Diffusion equation Partial differential equation Physics and Astronomy (miscellaneous) Applied Mathematics Compact finite difference Markov chain Monte Carlo 010103 numerical & computational mathematics 01 natural sciences Probability model Computer Science Applications 010101 applied mathematics Computational Mathematics symbols.namesake Modeling and Simulation Present method symbols Order (group theory) Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Journal of Computational Physics. 394:477-490 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2019.06.012 |
| Popis: | In this paper, the Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation is studied. Most of the previous methods are low in temporal and spatial accuracy order. Based on the idea of Monte Carlo Markov chain method and compact finite difference schemes, a probability model for solving the modified anomalous fractional sub-diffusion equation is established. Numerical examples are given to show the feasibility of the proposed scheme. Compared with the compact finite difference method, the present method is truly meshless and is easy to be implemented with high temporal and spatial accuracy order. And it is also applied to solve partial differential equation in irregular domains. |
| Databáze: | OpenAIRE |
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