[1]曾文平.解高阶抛物型方程的一族隐式差分格式[J].华侨大学学报(自然科学版),2005,26(3):235-238.[doi:10.3969/j.issn.1000-5013.2005.03.003]
　Zeng Wenping.A Family of Implicit Difference Schemes for Solving the Parabolic Equation of Higher Order[J].Journal of Huaqiao University(Natural Science),2005,26(3):235-238.[doi:10.3969/j.issn.1000-5013.2005.03.003]
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解高阶抛物型方程的一族隐式差分格式()
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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3期
页码:
235-238
栏目:
出版日期:
2005-07-20

文章信息/Info

Title:
A Family of Implicit Difference Schemes for Solving the Parabolic Equation of Higher Order
文章编号:
1000-5013(2005)03-0235-04
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:
高阶抛物型方程;  隐式差分格式;  稳定性
Keywords:
parabolic equation of higher order;  implicit difference scheme;  stability
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2005.03.003
文献标志码:
A
摘要:
对高阶抛物型方程t=(-1)m+1x2m(m为正整数),构造一族含双参数的三层隐式差分格式·在特殊情况下,当参数α=21,β=0时得到一个双层格式·这些格式的截断误差阶均为O((Δt)2+(Δx)4).证明当m=1,2,3时,这些格式对任意非负参数α≥0,β≥0都是绝对稳定的·数值例子表明,所得格式是有效的,其理论分析是正确的·
Abstract:
For solving the parabolic equation of higher order [SX(] u[] t[SX)]=(-1) m+1 [SX(] 2m u[] x 2m [SX)] (where m is a positive integer), a family of three-layered implicit difference schemes containing biparameters are constructed. In a special case, a two-layer scheme is obtained when parameter α=[SX(]1[]2[SX)], β=0. The order of the truncation error of all these schemes is O ((Δ t ) 2+(Δ x ) 4). These schemes are proved to be absolutely stable for arbitrarily chosen non-negative parameter α≥0, β ≥0 when m =1,2,3. As shown by numerical examples, these schemes are effective and the theoretical analysis is correct.

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(04QZR09)
更新日期/Last Update: 2014-03-23