Chebyshev tau matrix method for Poisson-type equations in irregular domain

Authors:
Weibin Kong;Xionghua Wu
Affiliations:
Department of Mathematics, Tongji University, Shanghai, 200092, PR China;Department of Mathematics, Tongji University, Shanghai, 200092, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, a new meshless method, Chebyshev tau matrix method (CTMM) is researched. The matrix representations for the differentiation and multiplication of Chebyshev expansions make CTMM easy to implement. Problems with curve boundary can be efficiently treated by CTMM. Poisson-type problems, including standard Poisson problems, Helmholtz problems, problems with variable coefficients and nonlinear problems are computed. Some numerical experiments are implemented to verify the efficiency of CTMM, and numerical results are in good agreement with the analytical one. It appears that CTMM is very effective for Poisson-type problems in irregular domains.