Chia-Cheng Tsai1, Chein-Shan Liu2, Wei-Chung Yeih3
CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.2, pp. 131-152, 2010, DOI:10.3970/cmes.2010.056.131
Abstract The fictitious time integration method (FTIM) previously developed by Liu and Atluri (2008a) is combined with the method of fundamental solutions and the Chebyshev polynomials to solve Poisson-type nonlinear PDEs. The method of fundamental solutions with Chebyshev polynomials (MFS-CP) is an exponentially-convergent meshless numerical method which is able to solving nonhomogeneous partial differential equations if the fundamental solution and the analytical particular solutions of the considered operator are known. In this study, the MFS-CP is extended to solve Poisson-type nonlinear PDEs by using the FTIM. In the solution procedure, the FTIM is introduced to convert a Poisson-type nonlinear PDE into… More >
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