摘要
以Hermite-Gauss节点为配置点,用带松弛因子的Hermite函数谱配置方法求数值解,逼近无界区域上的Kortewego-de Vries方程Cauchy问题的理论解,给出算法格式和相应的数值结果,表明所提算法格式的有效性和高精度。适当地选择松弛因子,使得数值解更好地匹配理论解的渐进行为,所给算法尤其适合于非线性问题。
The paper deals with the numerical solutions of initial value problem of KdV equation on un-bounded interval that approximates the solution of the Kortewego-de Vries equation,in which Hermite-Gauss nodes are used to collocate nodes of spectral collocation method.Selecting appro-priately the relaxation factor  involved in the generalized Hermite functions approximation enables us to fit the asymptotic behaviors of exact solutions at infinity closely.Numerical results demonstrate its efficiency and high accuracy of this approach.Especially,it is much easier to deal with nonlinear equation.
出处
《应用数学进展》
2019年第4期631-637,共8页
Advances in Applied Mathematics
基金
国家自然科学基金项目(11371123)
S201810464034.
