A meshless method for solving nonhomogeneous Cauchy problems |
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| Authors: | Ming Li C.S. Chen Y.C. Hon |
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| Affiliation: | 1. Department of Mathematics, Taiyuan University of Technology, Taiyuan, China;2. Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA;3. Department of Mathematics, City University of Hong Kong, China |
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| Abstract: | In this paper the method of fundamental solutions (MFS) and the method of particular solution (MPS) are combined as a one-stage approach to solve the Cauchy problem for Poisson's equation. The main idea is to approximate the solution of Poisson's equation using a linear combination of fundamental solutions and radial basis functions. As a result, we provide a direct and effective meshless method for solving inverse problems with inhomogeneous terms. Numerical results in 2D and 3D show that our proposed method is effective for Cauchy problems. |
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