一维半线性波动方程差分解的收敛性

数学季刊 ›› 1997, Vol. 12 ›› Issue (3): 35-40.

一维半线性波动方程差分解的收敛性

Institute of Computational and Applied Mathematics;Xiangtan University,Hunan,411105;Laboratory of ComputationalPhysics,Institute of Applied Phyics and Computational Mathematics,Beijing,100088;Graduate School of ChinaAcademy of Engineering Physics,Beijing,100088；Xinjiang C.P.College of Army Corps,Changji,Xinjiang

收稿日期:1995-08-29 出版日期:1997-09-30 发布日期:2024-11-22
基金资助:
The Project Supported by National Natural Science Foundation of China.

Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable

Institute of Computational and Applied Mathematics;Xiangtan University,Hunan,411105;Laboratory of ComputationalPhysics,Institute of Applied Phyics and Computational Mathematics,Beijing,100088;Graduate School of ChinaAcademy of Engineering Physics,Beijing,100088；Xinjiang C.P.College of Army Corps,Changji,Xinjiang

Received:1995-08-29 Online:1997-09-30 Published:2024-11-22
Supported by:
The Project Supported by National Natural Science Foundation of China.

摘要/Abstract

摘要： In this paper,the convergence and stability of the 'Leap-frog' finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).

关键词: , semilinear wave equation, Leap-frog finite difference scheme, convergence and stability

Abstract: In this paper,the convergence and stability of the 'Leap-frog' finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).

Key words: , semilinear wave equation, Leap-frog finite difference scheme, convergence and stability

中图分类号:

O175

鲁百年, 房少梅. 一维半线性波动方程差分解的收敛性[J]. 数学季刊, 1997, 12(3): 35-40.

Lu Bainian, Fang Shaomei. Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable[J]. Chinese Quarterly Journal of Mathematics, 1997, 12(3): 35-40.

[1]	林娟, 王传荣. 开口弧上核密度属H*的Cauchy奇异积分的稳定性[J]. 数学季刊, 2010, 25(2): 220-227.
[2]	杨宁, 杨晗. 半线性波动方程解的低正则局部存在性[J]. 数学季刊, 2006, 21(1): 49-56.
[3]	. [J]. 数学季刊, 2005, 20(3): 232-237.
[4]	孙清滢. 求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性[J]. 数学季刊, 2003, 18(2): 154-162.
[5]	程燕. 不动点定理在奇摄动非线性初值问题的套层解中的应用[J]. 数学季刊, 2003, 18(1): 103-107.
[6]	欧阳成, 韩祥临. 非线性方程奇摄动问题的激波解[J]. 数学季刊, 2002, 16(4): 27-33.
[7]	许勇, 石雄辉, 王顺利, 师义民. NA样本下截断型分布族参数的经验Bayes估计[J]. 数学季刊, 2002, 16(4): 43-47.
[8]	李登峰, 战阴伟 . 紧框架的一个注记[J]. 数学季刊, 2002, 16(4): 48-51.
[9]	冶成福, 张淑敏, 火博丰 . 与lK₁ ∪ (∪C_ui)的补图有相同色划分的图[J]. 数学季刊, 2002, 16(4): 52-56.
[10]	何楚宁 . 两类矩阵方程有亚半正定解的充要条件[J]. 数学季刊, 2002, 16(4): 62-68.
[11]	李林, 徐琛梅 . 一类非线性微分方程系统周期解的性[J]. 数学季刊, 2002, 16(4): 69-77.
[12]	杜炜 . 二阶非线性微分方程的振动性[J]. 数学季刊, 2002, 16(4): 87-93.
[13]	周桂云. 离散边值问题多重正解的存在性[J]. 数学季刊, 2002, 16(4): 99-104.
[14]	陈卫红, 曾洪杰. Galois环对Z_m环上一类逻辑函数的分析[J]. 数学季刊, 2002, 16(4): 105-110.
[15]	张福利 . 关于超半素环和超半素根的注记[J]. 数学季刊, 2002, 16(3): 105-106.