[1]曾文平.高阶演化方程任意阶精度的显式格式[J].华侨大学学报(自然科学版),2000,21(1):1-7.[doi:10.3969/j.issn.1000-5013.2000.01.001]
　Zeng Wenping.Explicit Difference Schemes of Higher Evolution Equation with Accuracy of Arbitrary Order[J].Journal of Huaqiao University(Natural Science),2000,21(1):1-7.[doi:10.3969/j.issn.1000-5013.2000.01.001]
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高阶演化方程任意阶精度的显式格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第21卷
期数:
2000年第1期
页码:
1-7
栏目:
出版日期:
2000-01-20

文章信息/Info

Title:
Explicit Difference Schemes of Higher Evolution Equation with Accuracy of Arbitrary Order
文章编号:
1000-5013(2000)01-0001-07
作者:
曾文平
华侨大学管理信息科学系, 泉州362011
Author(s):
Zeng Wenping
Dept. of Manag. Info. Sci., Huaqiao Univ., 362011, Quanzhou
关键词:
高阶演化方程;  高精度显式差分格式;  稳定性分析
Keywords:
higher evolution equation;  explicit difference scheme with high accuracy;  stability analysis
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2000.01.001
摘要:
讨论高阶演化方程 u t=a 2 k+ 1 u x2 k+ 1 (其中 a≠ 0为实常数,k=1,2,3,… )的 2层与 3层显式差分格式 .已有格式的精度是 O(τ+h)或 O(τ+h2 ) .利用半离散化方法给出一类具有任意阶精度 O(τp+hq) (p,q=1,2,… )的显式格式,讨论 p=3,4,q=2 k,2 (k+1 ),2 (k+2 ) (2层格式 )和 p=2,4,q=2 k,2 (k+1 ),2 (k+2 ) (3层格式 ) (k=1,2,3,4)的情况,导出两种格式的稳定性条件 .这些条件优于其它同类格式,且所得结果包含了前人的研究结果 .
Abstract:
A discussion is devoted to two level and three level explicit difference schemes of higher evolution equation u / t=a 2k+1 u / x 2k+1,where a ≠0 is real constant and k =1,2,3,… . In addition to the accuracy O(τ+h) and O(τ+h 2) of known schemes, a class of explicit schemes with accuracy of arbitrary order O(τ p+h q)(p,q=1,2,…) are given by using semi discrete method. From the discussion on the cases of two level scheme p=3,4, q=2k, 2(k+1), 2(k+2) and three level scheme p=2,4, q=2k, 2(k+1), 2(k+2)(k=1,2,3,4), the stability conditions of these schemes are derived. These conditions are better than those of similar schemes in reference (2). The author’s results involve the results in reference(3).

参考文献/References:

[1] 秦孟兆. 一类演化方程ut=αuqu1+aup的差分格式 [J]. 科学通报, 1982(5):261-263.
[2] 黎益, 廖晓峰. 色散方程的任意阶精度的显式差分格式 [J]. 四川大学学报(自然科学版), 1993(4):442-447.
[3] Lancaster P, Tisemestsky M. The theory of matrices [M]. New York:Academic Press, 1985.334-337.
[4] Richtmyer R D, Maorton K W. Difference methods for initial-value problems [M]. New York:John Wiley·Sons Inc, 1967.35-153.
[5] 秦孟兆. 波动方程两种哈密顿型蛙跳格式 [J]. 计算数学, 1988(3):272-281.

相似文献/References:

[1]曾文平,郑邵鹏.两类新的高稳定性的三层显式差分格式[J].华侨大学学报(自然科学版),1999,20(4):339.[doi:10.11830/ISSN.1000-5013.1999.04.0339]
　Zeng Wenping,Zheng Shaopeng.Two New Classes of Three-Level Explicit Difference Schemes with Higher Stability[J].Journal of Huaqiao University(Natural Science),1999,20(1):339.[doi:10.11830/ISSN.1000-5013.1999.04.0339]

备注/Memo

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