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

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 exponent...

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Bibliographic Details
Published in:Computer modeling in engineering & sciences 2010, Vol.56 (2), p.131-152
Main Authors: Chia-Cheng, Tsai, Liu, Chein-Shan, Wei-Chung Yeih
Format: Article
Language:English
Subjects:
Chebyshev approximation
Finite element method
Helmholtz equations
Mathematical analysis
Mathematical models
Meshless methods
Nonlinear differential equations
Nonlinearity
Numerical analysis
Numerical methods
Operators
Partial differential equations
Polynomials
Time integration
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Summary: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.
ISSN:1526-1492
1526-1506
DOI:10.3970/cmes.2010.056.131