Higher Order Compact Finite Difference Method For The Solution Of 2-D Time Fractional Diffusion Equation

Muhammad Usman (), Noor Badshah and Fazal Ghaffa
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Muhammad Usman: Department, of Basic Science & Islamiyat UET, Peshawar, Pakistan
Noor Badshah: Department, of Mathematics, Government Jehanzeb Post Graduate College Saidu Sharif Swat, KPK, Pakistan

Matrix Science Mathematic (MSMK), 2018, vol. 2, issue 1, 4-8

Abstract: The main purpose of this study is to work on the solution of two-dimensional time fractional diffusion equation In this research work we apply the HOC scheme to approximate the second order space derivative. To obtain a discrete implicit scheme, Grunwald-Letnikov descritization is used in sense to approximate the Riemann-Liouville time fractional derivative. The scheme thus obtained is based on block pentadiagonal matrix and each matrix has five-point stencil in order to reduce the computational cost we use AOS method. In AOS method, before taking the average of two solutions first we split the n-dimensional problems into a sum of n-one dimensional problem.

Keywords: FDE’s; HOC iterative scheme; AOS scheme; Convergence; Fourier analysis (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:zib:zbmsmk:v:2:y:2018:i:1:p:4-8

DOI: 10.26480/msmk.01.2018.04.08

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