TY - EJOU
AU - Tsai, Chia-Cheng
AU - Liu, Chein-Shan
AU - Yeih, Wei-Chung
TI - Fictitious Time Integration Method of Fundamental Solutions with Chebyshev Polynomials for Solving Poisson-type Nonlinear PDEs
T2 - Computer Modeling in Engineering \& Sciences
PY - 2010
VL - 56
IS - 2
SN - 1526-1506
AB - 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.
KW - Fictitious time integration method
KW - Method of fundamental solutions
KW - Chebyshev polynomial
KW - Nonlinear partial differential equation
DO - 10.3970/cmes.2010.056.131