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Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems

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  • Li, Xuhao
  • Wong, Patricia J.Y.

Abstract

In this paper, we propose a new numerical scheme for two-dimensional fractional sub-diffusion problems using non-polynomial spline. The solvability, stability and convergence of the proposed method are established using the well known discrete energy methodology. It is shown that the spatial convergence order is at least 4.5 which improves the best result achieved to date. We also carry out simulation to demonstrate the accuracy and efficiency of the proposed scheme and to compare with other methods.

Suggested Citation

  • Li, Xuhao & Wong, Patricia J.Y., 2019. "Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 222-242.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:222-242
    DOI: 10.1016/j.amc.2019.03.045
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    References listed on IDEAS

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    1. Ji, Cui-cui & Sun, Zhi-zhong, 2015. "The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 775-791.
    2. A. Khan & M. A. Noor & T. Aziz, 2004. "Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 309-322, August.
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