DERIVATION OF PARTICULAR SOLUTIONS USING CHEBYSHEV POLYNOMIAL BASED FUNCTIONS

作者：Chen, C S^*; Lee, Sungwook; Huang, C S

来源：International Journal of Computational Methods, 2007, 4(1): 15-32.

DOI：10.1142/S0219876207001096

• Particular solution
• method of fundamental solutions
• radial basis functions
• Chebyshev polynomial
• meshless methods
• multidimensional interpolation

In this paper, we propose a simple and direct numerical procedure to obtain particular solutions for various types of differential equations. This procedure employs the power series expansion of a differential operator. Chebyshev polynomials are selected as basis functions for the approximation of the inhomogeneous terms of the given partial differential equation. This numerical scheme provides a highly efficient and accurate approximation for the evaluation of a particular solution for a variety of classes of partial differential equations. To demonstrate the effectiveness of the proposed scheme, we couple the method of fundamental solutions to solve a modified Helmholtz equation with irregular boundary configuration. The solutions were observed to have high accuracy.

• 出版日期2007-3
• 单位中山大学