Comparison of Finite Difference Solution Methods for Reaction Diffusion System in Two Dimensions

Abstract

In this paper, we study three types of finite difference methods, to find the numerical solution of reaction difference systems of PDEs in two dimensions. These methods are ADE, ADI and Hopscotch, where Gray-Scott model in two dimensions has been considered. Our numerical results show that the ADI method produces more accurate and stable solution than ADE method and Hopscotch method is the best because does not involve any tridiagonal matrix. Also we studied the consistency, stability and convergence of the above methods.

Keywords

• gray-scott model in two dimensions
• finite difference methods
• alternating direction explicit method
• alternating direction implicit method
• hopscotch method