[1]单双荣.解四阶抛物型方程的高精度差分格式[J].华侨大学学报(自然科学版),2005,26(1):19-22.[doi:10.3969/j.issn.1000-5013.2005.01.005]
　Shan Shuangrong.Difference Schemes of High Accuracy for SolvingParabolic Equation of Four Order[J].Journal of Huaqiao University(Natural Science),2005,26(1):19-22.[doi:10.3969/j.issn.1000-5013.2005.01.005]
点击复制

解四阶抛物型方程的高精度差分格式()
分享到：

《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1期
页码:
19-22
栏目:
出版日期:
2005-01-20

文章信息/Info

Title:
Difference Schemes of High Accuracy for SolvingParabolic Equation of Four Order
文章编号:
1000-5013(2005)01-0019-04
作者:
单双荣
华侨大学数学系 福建泉州362011
Author(s):
Shan Shuangrong
Dept. of Math., Huaqiao Univ., 362011, Quanzhou, China
关键词:
四阶抛物型方程;  差分格式;  绝对稳定
Keywords:
parabolic equation of four order;  difference scheme;  absolutely stable
分类号:
O241.82
DOI:
10.3969/j.issn.1000-5013.2005.01.005
文献标志码:
A
摘要:
对四阶抛物型方程构造了一族含参数高精度三层差分格式 .当参数满足一定的条件时,差分格式稳定,局部截断误差阶数最高可达 O(τ2 +h6) .最后,用数值例子说明对稳定性所作的分析是正确的 .
Abstract:
A family of highly accurate and three layer difference schemes containing parameter are constructed for solving parabolic equation of four order. In case the parameter satisfies definite conditions, these difference schemes are stable, with the maximum order of local truncation error up to O(τ 2+h 6) . The stability analysis is shown by numerical example to be correct.

参考文献/References:

[1] СаулъевК, 袁兆鼎. 抛物型方程的网格积分法 [M]. 北京:科学出版社, 1963.143-152.
[2] 林鹏程. 解四阶抛物型方程的绝对稳定高精度差分格式 [J]. 厦门大学学报(自然科学版), 1994(6):756-759.
[3] 曾文平. 四阶抛物型方程两类新的恒稳差分格式 [J]. 华侨大学学报(自然科学版), 1997(4):334-340.
[4] 单双荣. 解四阶抛物型方程的高精度差分格式 [J]. 华侨大学学报(自然科学版), 2003(1):11-15.doi:10.3969/j.issn.1000-5013.2003.01.002.
[5] Richtmyer R D, Morton K W. Difference method for initial-value problems [M]. New York:wiley, 1967.59-91.

相似文献/References:

[1]梁敏.带耗散的气体动力学方程组的广义解存在性定理[J].华侨大学学报(自然科学版),1985,6(4):376.[doi:10.11830/ISSN.1000-5013.1985.04.0376]
　Liang Min.The Existent Theorems of Generalized Solutions for the Systems of Gas Dynamics with Dissipation[J].Journal of Huaqiao University(Natural Science),1985,6(1):376.[doi:10.11830/ISSN.1000-5013.1985.04.0376]
[2]曹文平.高阶Schrodinger方程的一类半隐式差分格式[J].华侨大学学报(自然科学版),1995,16(4):358.[doi:10.11830/ISSN.1000-5013.1995.04.0358]
　Zeng Wenping.A Class of Semi-Implicit Difference Schemes for Schrodinger Type Equation of Higher Order[J].Journal of Huaqiao University(Natural Science),1995,16(1):358.[doi:10.11830/ISSN.1000-5013.1995.04.0358]
[3]曾文平.解四阶抛物型方程高精度恒稳的隐式格式[J].华侨大学学报(自然科学版),1996,17(4):331.[doi:10.11830/ISSN.1000-5013.1996.04.0331]
　Zeng Wenping.A Class of High Accurate and Absolutely Stable Implicit Difference Schemes for Solving Four Order Parabolic Equations[J].Journal of Huaqiao University(Natural Science),1996,17(1):331.[doi:10.11830/ISSN.1000-5013.1996.04.0331]
[4]曾文平.解四阶抛物型方程的高精度显式差分格式[J].华侨大学学报(自然科学版),1997,18(2):122.[doi:10.11830/ISSN.1000-5013.1997.02.0122]
　Zeng Wenping.Explicit Difference Scheme of High Accuracy for Solving Four Order Parabolic Equation[J].Journal of Huaqiao University(Natural Science),1997,18(1):122.[doi:10.11830/ISSN.1000-5013.1997.02.0122]
[5]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),1997,18(3):225.[doi:10.11830/ISSN.1000-5013.1997.03.0225]
　Zeng Wenping.A Class of New Steady Difference Schemes for Convective Equation[J].Journal of Huaqiao University(Natural Science),1997,18(1):225.[doi:10.11830/ISSN.1000-5013.1997.03.0225]
[6]曾文平.四阶抛物型方程两类新的恒稳差分格式[J].华侨大学学报(自然科学版),1997,18(4):334.[doi:10.11830/ISSN.1000-5013.1997.04.0334]
[7]曾文平.解二维抛物型方程的恒稳高精度格式[J].华侨大学学报(自然科学版),1999,20(1):18.[doi:10.11830/ISSN.1000-5013.1999.01.0018]
　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(1):18.[doi:10.11830/ISSN.1000-5013.1999.01.0018]
[8]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.[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(1):122.[doi:10.3969/j.issn.1000-5013.2001.02.003]
[9]单双荣.高阶Schringer方程的显式差分格式[J].华侨大学学报(自然科学版),2002,23(1):12.[doi:10.3969/j.issn.1000-5013.2002.01.003]
　Shan Shuangrong.Explicit Difference Schemes for Solving Higher-Order Schringer Equation[J].Journal of Huaqiao University(Natural Science),2002,23(1):12.[doi:10.3969/j.issn.1000-5013.2002.01.003]
[10]曾文平.抛物型方程的一族双参数高精度恒稳格式[J].华侨大学学报(自然科学版),2002,23(4):327.[doi:10.3969/j.issn.1000-5013.2002.04.001]
[11]单双荣.解四阶抛物型方程的高精度差分格式[J].华侨大学学报(自然科学版),2003,24(1):11.[doi:10.3969/j.issn.1000-5013.2003.01.002]
　Shan Shuangrong.Difference Schemes of High Accuracy for SolvingParabolic Equation of Four Order[J].Journal of Huaqiao University(Natural Science),2003,24(1):11.[doi:10.3969/j.issn.1000-5013.2003.01.002]
[12]金相华,曾文平.解四阶抛物型方程的若干新的差分格式[J].华侨大学学报(自然科学版),2006,27(3):238.[doi:10.3969/j.issn.1000-5013.2006.03.004]
　Jin Xianghua,Zeng Wenping.Several New Difference Schemes for Solving Fourth Order Parabolic Equation[J].Journal of Huaqiao University(Natural Science),2006,27(1):238.[doi:10.3969/j.issn.1000-5013.2006.03.004]
[13]崔晓鹏,单双荣.解四阶抛物型方程的两层高精度差分格式[J].华侨大学学报(自然科学版),2011,32(6):710.[doi:10.11830/ISSN.1000-5013.2011.06.0710]
　CUI Xiao-peng,SHAN Shuang-rong.High-Accurate and Two-Layer Difference Schemes for Solving Four-Order Parabolic Equation[J].Journal of Huaqiao University(Natural Science),2011,32(1):710.[doi:10.11830/ISSN.1000-5013.2011.06.0710]

更新日期/Last Update: 2014-03-23