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A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations

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  • Yaseen, Muhammad
  • Abbas, Muhammad
  • Ismail, Ahmad Izani
  • Nazir, Tahir

Abstract

A cubic trigonometric B-spline collocation approach for the numerical solution of fractional sub-diffusion equation is presented in this paper. The approach is based on the usual finite difference scheme to discretize the time derivative while the approximation of the second-order derivative with respect to space is obtained by the cubic trigonometric B-spline functions with the help of Grünwald–Letnikov discretization of the Riemann–Liouville derivative. The scheme is shown to be stable using the Fourier method and the accuracy of the scheme is tested by application to a test problem. The results of the numerical test verify the accuracy and efficiency of the proposed algorithm.

Suggested Citation

  • Yaseen, Muhammad & Abbas, Muhammad & Ismail, Ahmad Izani & Nazir, Tahir, 2017. "A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 311-319.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:311-319
    DOI: 10.1016/j.amc.2016.08.028
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    References listed on IDEAS

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    1. Shazalina Mat Zin & Muhammad Abbas & Ahmad Abd Majid & Ahmad Izani Md Ismail, 2014. "A New Trigonometric Spline Approach to Numerical Solution of Generalized Nonlinear Klien-Gordon Equation," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-9, May.
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