定常对流扩散反应方程的指数型高阶差分格式  

High-order Exponential Finite Difference Method for 1D Convection-diffusion-reaction Equation

作　　者：魏剑英[1] 

机构地区：[1]宁夏大学 数学计算机学院,宁夏银川750021

出　　处：《宁夏大学学报（自然科学版）》2012年第2期140-143,共4页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10972058;11061025);教育部科学技术研究重点项目(210239);霍英东教育基金会高等院校青年教师基金资助项目(121105)

摘　　要：提出了一种数值求解一维定常对流扩散反应方程的指数型四阶差分格式.首先,由常数变易法求得模型方程的通解并应用到x_(i-1),x_i,x_(i+1)3点上,得到模型方程的指数型差分格式.然后,利用源项f(x)在点x_i处的二阶泰勒展开,得到定常对流扩散反应方程的指数型四阶差分格式.最后,用数值算例验证了该格式的高阶精度和可靠性.An exponential high-order difference scheme is proposed to solve the one-dimensional convection diffusion reaction equation. Firstly the model equation＇s general solution is got by using the variation of constants method, and an exponential difference scheme of the model equation is constructed by using of the exact solution evaluated at nodal points xi-1 ,xi and xi＋1 . And then, applying second-order Taylor expansion for source term, the final exponential high order difference scheme is obtained. The algorithm is verified by three numerical examples.

关 键 词：对流扩散反应方程 常数变易法 泰勒展开 指数型高阶差分格式 

分 类 号：O241.82[理学—计算数学]