Derivation of Particular Solutions Using Chebyshev Polynomial Based Functions
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.
International Journal of Computational Methods
(2007). Derivation of Particular Solutions Using Chebyshev Polynomial Based Functions. International Journal of Computational Methods, 4(1), 15-32.
Available at: https://aquila.usm.edu/fac_pubs/1790