广义对称正则长波方程的一个新的守恒差分逼近

广义对称正则长波方程的一个新的守恒差分逼近 A New Conservation Difference Approximation for Generalized Symmetric Regularized Long Wave Equation 陈利娅 CHEN Liya1 1 first-author 胡朝浪 HU Chaolang2 2 赖霞 LAI Xia1 1 西华大学数学与计算机学院 西华大学数学与计算机学院 School of Mathematics and Computer Engineering,Xihua University School of Mathematics and Computer Engineering,Xihua University 四川大学数学学院 四川大学数学学院 College of Mathematics,Sichuan University College of Mathematics,Sichuan University 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. 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 conservative scheme with two levels. 广义对称正则长波方程 差分格式 守恒 收敛性 稳定性 generalized symmetric regularized long wave （GSRLW） equation finite difference scheme conservation convergence stability 10.14188/j.1671-8836.2010.04.002 O241.82 国家自然科学基金资助项目（40701014） 2010-04-01 2021-04-01 4 56