Approximation of solutions of polynomial partial differential equations in two independent variables

A numerical method for solving polynomial partial differential equations in two independent variables, defined in the paper, is presented. The technique is based on polynomial approximation. Properties and the operational matrices for partial derivatives for a polynomial in two variables are presented first. These properties are then used to reduce the solution of partial differential equations in two independent variables to a system of algebraic equations. Five illustrative examples are presented to prove the effectiveness of the present method. Results show that the numerical scheme is very convenient for solving polynomial partial differential equations.