[1]黄浪扬,曾文平.抛物型方程的一族高精度恒稳格式[J].华侨大学学报(自然科学版),2000,21(2):124-128.[doi:10.3969/j.issn.1000-5013.2000.02.004]
　Huang langyang,Zeng Wenping.A Group of Steady Difference Schemes wth High Accuracy for Solving Parabolic Equation[J].Journal of Huaqiao University(Natural Science),2000,21(2):124-128.[doi:10.3969/j.issn.1000-5013.2000.02.004]
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抛物型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21卷
期数:
2000年第2期
页码:
124-128
栏目:
出版日期:
2000-04-20

文章信息/Info

Title:
A Group of Steady Difference Schemes wth High Accuracy for Solving Parabolic Equation
文章编号:
1000-5013(2000)02-0124-05
作者:
黄浪扬; 曾文平
华侨大学管理信息科学系, 泉州362011
Author(s):
Huang langyang;  Zeng Wenping
Dept. of Manag. Info. Sci., Huaqiao Univ., 362011, Quanzhou
关键词:
二阶抛物型方程;  绝对稳定;  高精度;  隐式差分格式
Keywords:
second order parabolic equation;  absolutely stable;  high accuracy;  implicit difference scheme
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2000.02.004
摘要:
对二阶抛物型方程 ut=uxx,构造了一族新的三层隐式差分格式 (在特殊情况下是两层 ) .它们含有非负参数α1,α2 和α3,其截断误差至少可达 O((Δt) 2 +(Δx) 4 ) .对三层格式,在条件α1 ≥α2 ≥0,α2 ≤ 12 及α1 +α2 +α3 =1之下绝对稳定 .特别地,在条件α1 =0,α2 =α3 或α1 =α2,α3 =0之下成为两层不含参数的隐式格式,且也是绝对稳定的 .这些格式均可用追赶法求解 .在该格式中,选取适当的参数,可得抛物型方程初边值差分格式中的高精度格式 .
Abstract:
A new group of three layer implicit differemce schemes, which can be two layer in special case, are constructed for solving second order parabolic equation where u t=u xx . They contain non negative parameter α 1, α 2 and α 3, with truncation error up to O ((Δ t ) 2+(Δ x ) 4) at least. Under the conditions of α 1≥ α 3≥0, α 2≤12 and α 1+ α 2+ α 3=1, these three layer schemes are absolutely stable. Under the conditions of α 1=0, α 2= α 3 or α 1= α 2, α 3=0 as a special case, they become two layer but remain absolutely stable. All these schemes can be solved by double sweeping method. By choosing proper parameter, highly accurate schemes in difference schemes with initial boundary value can be obtained for solving parabolic equation.

参考文献/References:

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更新日期/Last Update: 2014-03-23