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| A numerical approach for space-fractional diffusion equation by differential quadrature |
| Received:December 17, 2019 Revised:May 28, 2020 |
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| DOI：10.7511/jslx20191217002 |
| KeyWord:differential quadrature radial basis functions space-fractional diffusion equation |
| Author | Institution |
| 朱晓钢 |
邵阳学院 理学院, 邵阳 |
| 聂玉峰 |
西北工业大学 应用数学系, 西安 |
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| Abstract: |
| This article is devoted to develop a direct numerical approach for the space-fractional diffusion equation with variable coefficients by differential quadrature (DQ) technique.Two DQ approximations of fractional derivatives based on Reciprocal Multiquadric and Thin-Plate Spline radial basis functions(RBFs) are introduced and applied to turn the equation in consideration into a set of easily solvable ordinary differential equations,which are discretized by the Crank-Nicolson scheme.The presented methods are verified by five numerical examples and the numerical results illustrate that they outperform some existing algorithms in term of both accuracy and efficiency as long as the shape parameters of RBFs are properly chosen. |