Open Access

ARTICLE

Fictitious Time Integration Method of Fundamental Solutions with Chebyshev Polynomials for Solving Poisson-type Nonlinear PDEs

Chia-Cheng Tsai¹, Chein-Shan Liu², Wei-Chung Yeih³

1 Department of Marine Environmental Engineering, National Kaohsiung Marine University, Kaohsiung City 811, Taiwan (tsaichiacheng@mail.nkmu.edu.tw)
2 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
3 Department of Harbor & River Engineering and Computation and Simulation Center, National Taiwan Ocean University, Keelung, 202, Taiwan

Computer Modeling in Engineering & Sciences 2010, 56(2), 131-152. https://doi.org/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 a sequence of linear nonhomogeneous modified Helmholtz equations which are then formally solved by the MFS-CP. Several numerical experiments were carried out to validate the proposed methods.

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Keywords

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