Polynomial Particular Solutions for the Solutions of PDEs with Variables Coefficients (Advances in Applied Mathematics and Mechanics, 2018)
The closed-form particular solutions with polynomial basis functions forgeneral partial differential equations (PDEs) with constant coefficients have been derivedand applied for solving various kinds of problems in the context of the methodof approximate particular solutions (MAPS). In this paper, we propose to extend theabove-mentioned method to PDEs with variable coefficients by the substituting andadding-back technique. Since the linear system derived from the polynomial particularsolutions is notoriously ill-conditioned, the multiple scale method is applied toalleviate this difficulty. To validate our proposed method, four numerical examplesare considered and compared with those obtained by the MAPS using the radial basisfunctions.