(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
The closed-form particular solutions with polynomial basis functions for general partial differential equations (PDEs) with constant coefficients have been derived and applied for solving various kinds of problems in the context of the method of approximate particular solutions (MAPS). In this paper, we propose to extend the above-mentioned method to PDEs with variable coefficients by the substituting and adding-back technique. Since the linear system derived from the polynomial particular solutions is notoriously ill-conditioned, the multiple scale method is applied to alleviate this difficulty. To validate our proposed method, four numerical examples are considered and compared with those obtained by the MAPS using the radial basis functions.