The Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation

Zhi Zhong Yan; Cheng Feng Zheng; Chuanzeng Zhang

doi:10.1016/j.jcp.2019.06.012

The Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation

Zhi Zhong Yan^*, Cheng Feng Zheng, Chuanzeng Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	477-490
Number of pages	14
Journal	Journal of Computational Physics
Volume	394
DOIs	https://doi.org/10.1016/j.jcp.2019.06.012
Publication status	Published - 1 Oct 2019

Keywords

Compact finite difference scheme
Irregular domain
Modified anomalous fractional sub-diffusion equation
Monte Carlo Markov chains

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10.1016/j.jcp.2019.06.012

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title = "The Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation",

abstract = "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.",

keywords = "Compact finite difference scheme, Irregular domain, Modified anomalous fractional sub-diffusion equation, Monte Carlo Markov chains",

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AU - Yan, Zhi Zhong

AU - Zheng, Cheng Feng

AU - Zhang, Chuanzeng

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Compact finite difference scheme

KW - Irregular domain

KW - Modified anomalous fractional sub-diffusion equation

KW - Monte Carlo Markov chains

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M3 - Article

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SN - 0021-9991

VL - 394

SP - 477

EP - 490

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

The Monte Carlo Markov chain method for solving the modified anomalous fractional sub-diffusion equation

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Keywords

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