Simulations of nonlinear parabolic PDEs with forcing function without linearization

Abstract

Abstract This paper aims at producing numerical solutions of nonlinear parabolic PDEs with forcing term without any linearization. Since the linearization of nonlinear term leads to lose real features, without doing linearization, this paper focuses on capturing natural behaviour of the mechanism. Therefore we concentrate on analysis of the physical processes without losing their properties. To carry out this study, a backward differentiation formula in time and a spline method in space have been combined in leading to the discretized equation. This method leads to a very reliable alternative in solving the problem by conserving the physical properties of the nature. The efficiency of the present method are proved theoretically and illustrated by various numerical tests.