[1]单双荣.二维抛物型方程的高稳定性两层显式格式[J].华侨大学学报(自然科学版),2008,29(4):622-626.[doi:10.11830/ISSN.1000-5013.2008.04.0622]
　SHAN Shuang-rong.Two-Level Explicit Difference Schemes with Higher Stability Properties for Solving the Equation of Two-Dimensional Parabolic Type[J].Journal of Huaqiao University(Natural Science),2008,29(4):622-626.[doi:10.11830/ISSN.1000-5013.2008.04.0622]
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二维抛物型方程的高稳定性两层显式格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第29卷
期数:
2008年第4期
页码:
622-626
栏目:
出版日期:
2008-10-20

文章信息/Info

Title:
Two-Level Explicit Difference Schemes with Higher Stability Properties for Solving the Equation of Two-Dimensional Parabolic Type
文章编号:
1000-5013(2008)04-0622-05
作者:
单双荣
华侨大学数学科学学院
Author(s):
SHAN Shuang-rong
School of Mathematics Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
二维抛物型方程;  两层显式差分格式;  耗散项;  稳定性;  收敛性
Keywords:
equation of two-dimensional parabolic type;  two-level explicit difference scheme;  dissipative term;  stability;  convergence
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.2008.04.0622
文献标志码:
A
摘要:
利用加耗散项的方法,通过选取适当参数,构造二维抛物型方程的若干两层显式差分格式.其局部截断误差阶为O(τ+h2),而稳定性条件最好为r=(ΔΔxt)2=(ΔΔyt)2=hτ2≤1,优于(或不亚于)其他两层显格式,且这些格式都是简洁实用的两层显格式.数值试验表明,所做的稳定性分析是正确的.
Abstract:
By introducing dissipative term into conventional explicit schemes and choosing apropos parameter,several two-level explicit difference schemes are established for solving the equation of two-dimensional parabolic type.The order of the local discretization is O(τ+h2) and best stability condition is r=Δt(Δx)2=Δt(Δy)2=τh2≤1,which is better than(or equal to) the order by other two level explicit schemes.The schemes are also simple and practical explicit two-level difference schemes.The stability analysis made by the author is clearly stabled by numerical example.

参考文献/References:

[1] 南京大学. 偏微分方程数值解法 [M]. 北京:科学出版社, 1979.75-77.
[2] 马明书. 二维抛物型方程的一族两层显式格式 [J]. 河南师范大学学报(自然科学版), 2002(1):23-25.doi:10.3969/j.issn.1000-2367.2002.01.004.
[3] 金承日, 刘家琦. 关于二维热传导方程的一族显式格式 [J]. 哈尔滨工业大学学报, 1995(5):9-12.

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　Zeng Wenping.A Family of Steady and High Accurate Difference Schemes for Solving Two Dimensional Equations of Parabolic Type[J].Journal of Huaqiao University(Natural Science),1999,20(4):18.[doi:10.11830/ISSN.1000-5013.1999.01.0018]
[2]曾文平.二维抛物型方程精细积分法与差分法比较[J].华侨大学学报(自然科学版),2002,23(1):5.[doi:10.3969/j.issn.1000-5013.2002.01.002]
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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