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

• Published in: Journal of computational and applied mathematics Vol. 228; no. 1; pp. 158 - 167
• Main Authors: Kong, Weibin, Wu, Xionghua
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01-06-2009; Elsevier
• Subjects: Algebra; Chebyshev tau matrix method; Exact sciences and technology; Finite differences and functional equations; Irregular domain; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematics; Meshless; Numerical analysis; Numerical analysis. Scientific computation; Poisson-type equation; Sciences and techniques of general use; Sequences, series, summability; Poisson-type equation; Irregular domain; Chebyshev tau matrix method; Meshless; Multiplication; Numerical analysis; Applied mathematics; Poisson equation; Matrix method; Nonlinear problems; Matrix equation; Implementation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2008.09.011

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.