%0 Journal Article
%T 求解一维扩散反应方程的隐式高精度紧致差分格式<br>An Implicit High-Order Compact Difference Scheme for Solving the 1D Diffusion-Reaction Equation
%A 黄文姣
%A 巨月娟
%A 葛永斌&lt
%A br&gt
%A HUANG Wen-jiao
%A JU Yue-juan
%A GE Yong-bin
%J 西南大学学报(自然科学版)
%D 2018
%R 10.13718/j.cnki.xdzk.2018.07.013
%X 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<i>Ο</i>（<i>τ</i><sup>4</sup>+<i>h</i><sup>4</sup>），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.<br>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 <i>Ο</i>(<i>τ</i><sup>4</sup>+<i>h</i><sup>4</sup>), 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
%K 扩散反应方程
%K 高精度
%K 隐格式
%K 紧致格式
%K 有限差分法&lt
%K br&gt
%K diffusion-reaction equation
%K high accuracy
%K implicit scheme
%K compact scheme
%K finite difference method
%U http://xbgjxt.swu.edu.cn/jsuns/html/jsuns/2018/7/20180713.htm