Volume 11, Issue 2 (11-2016)
IJMSI 2016, 11(2): 71-86 |
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Nasrollahzadeh F, Hosseini S M. An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation. IJMSI 2016; 11 (2) :71-86
URL: http://ijmsi.ir/article-1-492-en.html
URL: http://ijmsi.ir/article-1-492-en.html
Abstract:
Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditional stability, and therefore first-order convergence of the method are proven. Some numerical examples with
known exact solution are tested, and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.
Keywords: Two-dimensional fractional differential equation, Space-time fractional diffusion equation, Implicit difference method, Alternating directions implicit methods
Type of Study: Research paper |
Subject:
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