Numerical modelling of linear and nonlinear diffusion equations by compact finite difference method

Abstract

In this work, accurate solutions to linear and nonlinear diffusion equations were introduced. A combination of a sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time have been used for treatment of these equations. The computed results with the use of this technique have been compared with the exact solution to show the accuracy of it. Here, the approximate solution to the diffusion equations has been obtained easily and elegantly with neither transforming nor linearizing the equation. The present method is seen to be a very good alternative method to some existing techniques for realistic problems. © 2010 Elsevier Inc. All rights reserved.