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

Xuhao Li and Patricia J.Y. Wong

Applied Mathematics and Computation, 2019, vol. 357, issue C, 222-242

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.

Keywords: Non-polynomial spline; Two-dimensional; Sub-diffusion equation; Fractional differential equation; Numerical solution (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:357:y:2019:i:c:p:222-242

DOI: 10.1016/j.amc.2019.03.045

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