奇异退化扩散反应方程的高阶紧致差分及网格自适应方法

计算物理 ›› 2017, Vol. 34 ›› Issue (3): 309-319.

奇异退化扩散反应方程的高阶紧致差分及网格自适应方法

葛永斌, 蔡志权

宁夏大学数学计算机学院, 宁夏银川 750021

收稿日期:2016-03-11 修回日期:2016-06-13 出版日期:2017-05-25 发布日期:2017-05-25
作者简介:葛永斌(1975-),男,宁夏,博导,研究方向为偏微分方程数值解法及科学计算可视化,E-mail:gyb@nxu.edu.cn;蔡志权(1989-),男,宁夏,硕士生,研究方向为偏微分方程数值解法,E-mail:caizhi1989@163.com
基金资助:
国家自然科学基金（11361045，11161036）及宁夏高等学校科学技术研究项目（NGY2013019）资助

High-order Compact Difference Schemes and Adaptive Method for Singular Degenerate Diffusion-Reaction Equations

GE Yongbin, CAI Zhiquan

School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received:2016-03-11 Revised:2016-06-13 Online:2017-05-25 Published:2017-05-25

摘要/Abstract

摘要： 利用余项修正法建立奇异退化扩散反应方程非均匀网格上的高阶紧致差分式，其时间具有二阶精度，空间具有三阶至四阶精度. 利用等分布原理建立时间和空间的网格自适应方法.最后通过具有精确解的数值算例验证方法的可靠性和精确性，并研究一维爆破问题.

关键词: 奇异退化扩散反应方程, 自适应方法, 非均匀网格, 高精度紧致格式, 爆破

Abstract: We established a high-order compact scheme on nonuniform grids for singular degenerate diffusion reaction equation. The scheme is second order accuracy in time and third to fourth order accuracy in space. A grid adaptive method is established by using equidistribution principle. Finally,a numerical example with exact solution validates reliability and accuracy of the method. One-dimentional blow up problem was solved with the method.

Key words: singular and degenerate diffusion-reaction equation, adaptive method, nonuniform grid, high order compact scheme, blow up

中图分类号:

O241.82

葛永斌, 蔡志权. 奇异退化扩散反应方程的高阶紧致差分及网格自适应方法[J]. 计算物理, 2017, 34(3): 309-319.

GE Yongbin, CAI Zhiquan. High-order Compact Difference Schemes and Adaptive Method for Singular Degenerate Diffusion-Reaction Equations[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(3): 309-319.

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