求解一维扩散反应方程的隐式高精度紧致差分格式  

An Implicit High-Order Compact Difference Scheme for Solving the 1D Diffusion-Reaction Equation

作　　者：黄文姣 巨月娟 葛永斌[1] HUANG Wen-jiao;JU Yue-juan;GE Yong-bin(Institute of Applied Mathematics and Mechanics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学应用数学和力学研究所,银川750021

出　　处：《西南大学学报（自然科学版）》2018年第7期85-90,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11772165);宁夏自然科学基金重点项目(2018AAC02003)

摘　　要：提出了一维扩散反应方程的一种隐式高精度紧致差分格式,空间二阶导数采用四阶紧致差分格式进行离散,时间导数采用四阶向后欧拉公式进行离散,格式截断误差为Ο(τ~4+h^4),即时间和空间都可以达到四阶精度,最后通过数值实验验证了本文方法的精确性和可靠性.In this paper,an implicit high accuracy compact difference scheme for solving the one-dimensional reaction-diffusion equation is proposed.The fourth-order compact difference scheme is adopted to discretize the second derivative in space,while the fourth-order backward Euler formula is used for discretization of time derivative.The truncation error of this scheme is Ο（τ^4＋h^4）,i.e,it is the fourth-order accuracy in both time and space.The accuracy and reliability of the present scheme is validated by some numerical experiments.

关 键 词：扩散反应方程 高精度 隐格式 紧致格式 有限差分法 

分 类 号：O241.82[理学—计算数学]