A Gauss-Galerkin finite-difference method for singular partial differential equations in two space variables

Abstract

A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss–Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are presented. These numerical results are encouraging and suggest that the proposed method is efficient in treating singular parabolic partial differential equations of the type considered here. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 331–355, 1997