Numerical solution of Two Dimension (2D) reaction diffusion equation with Compact finite difference method

Abstract

This study represents a numerical solution of two-dimensional reaction-diffusion equation(RDE).The reaction-diffusion equation is one of the most important partial differential equation(PDEs),and its applications can be found in many fields,including biology,chemistry,physics,finance and so on. Therefore,numerical simulation must be applied in order to solve RDE.In this line ,our aim is to develop compact finite difference of fourth order to solve two-dimensional RDE. In order to derive the method , we used Taylor series expansion, because the Taylor series expansion is always used to obtain higher order approximation of derivatives. Accordingly,in order to derive a compact finite dif ference four order, we replace derivatives by the difference equation using Taylor series expansion .Then ,we obtain fourth order central difference in spaces and a first order forward difference in time, which is a fourth order compact finite difference.The convergence of the developed scheme have been investigated.To demonstrated effectiveness of our proposed method , some examples of two dimensional RDE are presented. the obtained results are in good agreement with exact solutions. Besides, a graphical representation is given to observe the behavior of the obtained solutions. Based on the obtained results, the present method implies that it is well suited,simple,straightforward, and found to be a better mathematical technique to solve two-dimensional RDE.