A Study of a Non-linear Reaction Diffusion Equation Representing Initial and Boundary Value Problems by LDTM

Abstract: In this paper, we study the exact solutions of non-linear Reaction-Diffusion equation using the Laplace-Differential Transform method (LDTM). We apply Laplace transform in time domain and differential transform in space domain using initial and boundary conditions. We find that this method requires straightforward differentiation and a few elementary operations for the solution unlike other typical methods which requires integration. Illustrative examples are presented to demonstrate the applicability and efficiency of the technique. The concluding results are accurate and with less computational effort than some existing studies.

Keywords: LDTM, Non-linear Reaction-Diffusion equation, Initial Conditions, Boundary conditions.