A boundary meshless method using Chebyshev interpolation and trigonometric basis function for solving heat conduction problems

A boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two-stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution, respectively. As a result, no fundamental solution is required and the closed form of approximate particular solution is easy to obtain. The effectiveness of the proposed computational scheme is demonstrated by several examples in 2D and 31). We also compare our proposed method with the finite-difference method and the other meshless method showed in Sarler and Vertnik (Comput. Math. Appl. 2006; 51:1269-1282). Excellent numerical results have been observed. Copyright (C) 2007 John Wiley & Sons, Ltd.