[1]曾文平.一类演化方程的一族高精度恒稳差分格式[J].华侨大学学报(自然科学版),2005,26(1):11-15.[doi:10.3969/j.issn.1000-5013.2005.01.003]
　Zeng Wenping.A Family of Absolutely Stable Difference Schemes of High Accuracy for Solving a Class of Evolution Equations[J].Journal of Huaqiao University(Natural Science),2005,26(1):11-15.[doi:10.3969/j.issn.1000-5013.2005.01.003]
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一类演化方程的一族高精度恒稳差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第26卷
期数:
2005年第1期
页码:
11-15
栏目:
出版日期:
2005-01-20

文章信息/Info

Title:
A Family of Absolutely Stable Difference Schemes of High Accuracy for Solving a Class of Evolution Equations
文章编号:
1000-5013(2005)01-0011-05
作者:
曾文平
华侨大学数学系 福建泉州362021
Author(s):
Zeng Wenping
Department of Mathematics, Huaqiao University, 362021, Quanzhou, China
关键词:
演化方程;  差分格式;  高精度;  绝对稳定
Keywords:
evolution equation;  difference scheme;  high accuracy;  absolutely stable
分类号:
O175
DOI:
10.3969/j.issn.1000-5013.2005.01.003
文献标志码:
A
摘要:
对一类演化方程 u t=a 2m + 1 x1m + 1(a为常数,m =1,2,… ),构造一族含双参数的三层高精度隐式差分格式 .当参数α =12,β =0时,得到一个双层格式 证明对一切正整数m,该格式对任意非负参数α≥ 0,β≥ 0都是绝对稳定的,并且其截断误差阶为O((Δt) 2 +(Δx) 6) .数值例子表明,所建立的差分格式是有效的,理论分析与实际计算相吻合
Abstract:
A family of three layered and highly accurate implicit difference schemes containing two parameters are constructed for solving a class of evolution equations  u  t=a  2m+1  x 1m+1,where a is a constant, m equals to 1, 2, …. A two layered scheme is obtained when parameters α =1/2, β =0. These schemes are proved to be absolutely stable for all positive integers m and for arbitrarily chosen non negative parameters α≥0, β ≥0; and their truncation errors are all in the order of O(( Δ t) 2+( Δ x) 6) . The difference schemes establishing in this paper are shown by numerical examples to be effective, their practical computation is shown to be consistent with theoretical analysis.

参考文献/References:

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备注/Memo

备注/Memo:
国务院侨务办公室科研基金资助项目(04ZQR09)
更新日期/Last Update: 2014-03-23