[1]陈世平,曾文平.对流方程的一族高精度恒稳格式[J].华侨大学学报(自然科学版),2001,22(2):122-127.[doi:10.3969/j.issn.1000-5013.2001.02.003]
　Chen Shiping,Zeng Wenping.A Group of Steady Schemes with High Accuracy for Solving Convective Equation[J].Journal of Huaqiao University(Natural Science),2001,22(2):122-127.[doi:10.3969/j.issn.1000-5013.2001.02.003]
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对流方程的一族高精度恒稳格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第22卷
期数:
2001年第2期
页码:
122-127
栏目:
出版日期:
2001-04-20

文章信息/Info

Title:
A Group of Steady Schemes with High Accuracy for Solving Convective Equation
文章编号:
1000-5013(2001)02-0122-06
作者:
陈世平; 曾文平
泉州师范学院数学系, 泉州362001; 华侨大学经济管理学院, 泉州362011
Author(s):
Chen Shiping1;  Zeng Wenping2
1.Dept. of Math., Quanzhou Normal College, 362000, Quanzhou; 2.College of Econ. Manag., Huaqiao Univ., 362011, Quanzhou
关键词:
对流方程;  差分格式;  绝对稳定
Keywords:
convective equation;  difference scheme;  absolutely stable
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2001.02.003
摘要:
为求解对流方程 ut=aux 构造一族新的含 3参数 3层隐式差分格式 (在特殊情况下是 2层 ),其截断误差至少可达 O[( Δt) 2 +( Δx) 4].在条件 α1=α3,|α2 |≤ 2 |α1|或 α1≥ 0,α2 ≥ 0,α3≥ 0,α1>α3,α1+α2 +α3=1,α2 ≤ 1/ 2之下,绝对稳定 .特别地,当参数 α1=α2,α3=0时得到一个两层恒稳的差分格式 .所有这些格式都可用追赶法求解,它包含对流方程的已有文献中的隐式高精度恒稳格式 .
Abstract:
For solving convective equation u t=au x, a new group of implicit different schemes containing three parameters are constructed. They are three layers in general and two layers in special case. Their truncation error wile reach O [(Δ t ) 2+(Δ x ) 4] at least. Under the conditions of α 1=α 3,|α 2|≤2|α 1| or α 1≥0, α 2≥0, α 3≥0,α 1>α 3, α 1+α 2+α 3=1,α 2≤12,they are absolutely stable. Particalarly, a two layer steady difference scheme can be obtained in case parameter α 1=α 2,α 3=0 . All these schemes, with all steady ones with high accaracy in literatures included, can be solved by applying double sweeping method.

参考文献/References:

[1] MILLER J J H. On the location of zeros of certain classes of polynomials with application to numerical analy sis [J]. Journal of the Institute of Mathematics and Its Applications, 1971.394-406.
[2] Richtmyer R D, Morton K W. Difference methods for initial value problems. 2nd ed [M]. New York:wiley, 1967.36-108.
[3] 陆金甫, 关治. 偏微分方程数值解法 [M]. 北京:清华大学出版社, 1987.50-130.
[4] 曾文平. 对流方程的一类新的恒稳差分格式 [J]. 华侨大学学报(自然科学版), 1997(3):225-230.

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备注/Memo

备注/Memo:
福建省自然科学基金
更新日期/Last Update: 2014-03-23