| 广义对称正则长波方程的一个新的守恒差分逼近 |
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| 引用本文： | 陈利娅,胡朝浪,赖霞.广义对称正则长波方程的一个新的守恒差分逼近[J].武汉大学学报(理学版),2010,56(4). |
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| 作者姓名： | 陈利娅 胡朝浪 赖霞 |
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| 作者单位： | 1. 西华大学,数学与计算机学院,四川,成都,610039
2. 四川大学数学学院,四川,成都,610064 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 对一类广义对称正则长波(generalized symmetrical regularized long wave,GSRLW)方程的初边值问题进行了数值研究,提出了一个三层有限差分格式,并利用离散泛函分析方法分析了该格式的二阶收敛性与无条件稳定性,格式合理地模拟了初边值问题的守恒性质.数值结果表明,本文的三层格式具有二阶收敛性;与两层的守恒格式相比计算精度有了进一步的提高.
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| 关 键 词： | 广义对称正则长波方程 差分格式 守恒 收敛性 稳定性 |
A New Conservation Difference Approximation for Generalized Symmetric Regularized Long Wave Equation |
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| CHEN Liya,HU Chaolang,LAI Xia.A New Conservation Difference Approximation for Generalized Symmetric Regularized Long Wave Equation[J].JOurnal of Wuhan University:Natural Science Edition,2010,56(4). |
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| Authors: | CHEN Liya HU Chaolang LAI Xia |
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| Affiliation: | CHEN Liya1,HU Chaolang2,LAI Xia1(1.School of Mathematics and Computer Engineering,Xihua University,Chengdu 610039,Sichuan,China,2.College of Mathematics,Sichuan University,Chengdu 610064,China) |
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| Abstract: | The numerical solution for an initial-boundary value problem of generalized symmetric regularized long wave (GSRLW) equation is considered. A finite difference scheme of three levels is proposed. This scheme simulates the conservation properties of the problem well. It is proved that the finite difference scheme is convergent with order 2 and stable without condition by discrete functional analysis method. The numerical examples show this scheme is convergent with order 2 and has higher precision than the c... |
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| Keywords: | generalized symmetric regularized long wave (GSRLW) equation finite difference scheme conservation convergence stability |
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