Solving Stiff Reaction-Diffusion Equations Using Exponential Time Differences Methods  

作　　者：H. A. Ashi 

机构地区：[1]The Mathematical Department, King AbdulAziz University, Jeddah, KSA

出　　处：《American Journal of Computational Mathematics》2018年第1期55-67,共13页美国计算数学期刊（英文）

摘　　要：Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Though, this paper shows that recent advance methods can be more favored. In this work, we have incorporated, throughout numerical comparison experiments, spectral methods, for the space discretization, in conjunction with second and fourth-order time integrating methods for approximating the solution of the reaction-diffusion differential equations. The results have revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of implementation, accuracy and CPU time.Reaction-diffusion equations modeling Predator-Prey interaction are of current interest. Standard approaches such as first-order (in time) finite difference schemes for approximating the solution are widely spread. Though, this paper shows that recent advance methods can be more favored. In this work, we have incorporated, throughout numerical comparison experiments, spectral methods, for the space discretization, in conjunction with second and fourth-order time integrating methods for approximating the solution of the reaction-diffusion differential equations. The results have revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of implementation, accuracy and CPU time.

关 键 词：Finite DIFFERENCE METHODS EXPONENTIAL INTEGRATOR EXPONENTIAL Time Differencing Method REACTION-DIFFUSION System 

分 类 号：O1[理学—数学]