Alternating-direction implicit finite difference methods for a new two-dimensional two-sided space-fractional diffusion equation

Autor:	Xiucao Yin, Shaomei Fang, Changhong Guo
Jazyk:	angličtina
Rok vydání:	2018
Předmět:	Two-dimensional two-sided space-fractional diffusion equations The shifted left Grünwald formula The standard right Grünwald formula ADI methods Richardson extrapolation Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2018, Iss 1, Pp 1-17 (2018)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-018-1836-z
Popis:	Abstract According to the principle of conservation of mass and the fractional Fick’s law, a new two-sided space-fractional diffusion equation was obtained. In this paper, we present two accurate and efficient numerical methods to solve this equation. First we discuss the alternating-direction finite difference method with an implicit Euler method (ADI–implicit Euler method) to obtain an unconditionally stable first-order accurate finite difference method. Second, the other numerical method combines the ADI with a Crank–Nicolson method (ADI–CN method) and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. Finally, numerical solutions of two examples demonstrate the effectiveness of the theoretical analysis.
Databáze:	Directory of Open Access Journals
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