A Kansa-type MFS scheme for two-dimensional time fractional diffusion equations |
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Authors: | Liang Yan Fenglian Yang |
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Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing 210096, China;2. College of Science, Hohai University, Nanjing 210098, China |
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Abstract: | In this paper, an efficient Kansa-type method of fundamental solutions (MFS-K) is extended to the solution of two-dimensional time fractional sub-diffusion equations. To solve initial boundary value problems for these equations, the time dependence is removed by time differencing, which converts the original problems into a sequence of boundary value problems for inhomogeneous Helmholtz-type equations. The solution of this type of elliptic boundary value problems can be approximated by fundamental solutions of the Helmholtz operator with different test frequencies. Numerical results are presented for several examples with regular and irregular geometries. The numerical verification shows that the proposed numerical scheme is accurate and computationally efficient for solving two-dimensional fractional sub-diffusion equations. |
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Keywords: | Fractional differential equations Meshless method Method of fundamental solutions Finite differences |
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