高阶紧致格式结合外推技巧求解对流扩散方程

J4 ›› 2011, Vol. 46 ›› Issue (12): 39-43.

高阶紧致格式结合外推技巧求解对流扩散方程

钱凌志¹, 顾海波²

1. 石河子大学理学院数学系, 新疆石河子 832003;
2. 新疆师范大学数学科学学院, 新疆乌鲁木齐 830053

收稿日期:2010-11-23 出版日期:2011-12-20 发布日期:2011-12-24
作者简介:钱凌志(1980- ),男,硕士,讲师,主要从事偏微分方程理论与计算. Email:qianlingzhi@shzu.edu.cn
基金资助:
新疆维吾尔自治区自然科学基金资助项目(2010211B12)

High order compact scheme combined with extrapolation technique for solving convection-diffusion equations

QIAN Ling-zhi¹, GU Hai-bo²

1. Department of Mathematics, School of Science, Shihezi University, Shihezi 832003, Xinjiang, China;
2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830053, Xinjiang, China

Received:2010-11-23 Online:2011-12-20 Published:2011-12-24

摘要/Abstract

摘要：

将Padé 逼近方法、Richardson外推技巧、两重网格算法与紧致差分方法相结合,对线性对流扩散问题构造了一种新的高阶紧致差分格式,给出了格式的实现过程和误差估计,分析了稳定性。最后给出数值算例说明算法的有效性。

关键词: 紧致差分格式;Richardson外推技巧;两重网格算法;Padé逼近

Abstract:

Compact difference scheme are constructed by means of Padé approximation method, Richardson extrapolation technique and two-grid algorithm combined with compact finite difference scheme for linear convection-diffusion problems. Realization of the scheme,analysis of stability and error estimated are presented. Finally, numerical examples are presented to clarify the method.

Key words: compact difference scheme; Richardson extrapolation technique; twogrid algorighm; Padé approximation

钱凌志1, 顾海波2. 高阶紧致格式结合外推技巧求解对流扩散方程[J]. J4, 2011, 46(12): 39-43.

QIAN Ling-zhi1, GU Hai-bo2. High order compact scheme combined with extrapolation technique for solving convection-diffusion equations[J]. J4, 2011, 46(12): 39-43.

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