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

Author

Listed:
  • 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)

  • Fazal Ghaffa

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.

Suggested Citation

  • Muhammad Usman & Noor Badshah & Fazal Ghaffa, 2018. "Higher Order Compact Finite Difference Method For The Solution Of 2-D Time Fractional Diffusion Equation," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 4-8, January.
    • Handle: RePEc:zib:zbmsmk:v:2:y:2018:i:1:p:4-8
    DOI: 10.26480/msmk.01.2018.04.08
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