An efficient B-spline difference method for solving system of nonlinear parabolic PDEs

Abstract

This article tries to use of cubic B-spline collocation method in the form of a difference method to solving system of one dimension nonlinear parabolic partial differential equations. This method is characterized by the simplicity of the finite difference method through discussion of various parabolic pde problems, but does not have complex computation of traditional cubic B-spline collocation method. The use of this method leads to a system of algebraic equations which is suitable for computer programming. The stability and convergence of this method is discussed. The obtained numerical solutions indicate that the method is reliable and yields results compatible with the exact solutions. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization.