求解Benjamin-Bona-Mahony方程的拟紧致差分格式
Pseudo-compact difference scheme for Benjamin-Bona-Mahony equation
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摘要: 对Benjamin-Bona-Mahony(BBM)方程的初边值问题进行了数值研究,提出了一个3层拟紧致隐式差分格式,讨论了差分解的存在唯一性,并利用离散泛函分析方法分析了该格式的二阶收敛性与稳定性,并利用数值实验进行了验证.Abstract: The numerical solution for an initial-boundary value problem of Benjamin-Bona-Mahony equation was considered.Apseudo-compact finite difference of three levels was proposed.The existence and u-niqueness of solution are studied.It is proved that the finite difference scheme is convergent with the convergence order 2 and stable by the discrete functional analysis.And the results are demonstrated by the numerical examples.