微分求积法的一类线性多步法  

A Class of Linear Multistep Formula of Differential Quadrature Method

作　　者：刘冬兵 王永 林宗兵 LIU Dong-bing;WANG Yong;LIN Zong-bing(College of Mathematics and Computer,Panzhihua University,Panzhihua 617000,China;UHV Converter Station Branch of State Grid Shanghai Municipal Electric Power Company,Shanghai 201413,China)

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000 [2]国网上海市电力公司特高压换流站分公司,上海201413

出　　处：《数学的实践与认识》2021年第15期256-263,共8页Mathematics in Practice and Theory

基　　金：四川省科技厅应用基础研究项目(2019YJ0683);攀枝花市市级科研项目(2019ZD-R-1);攀枝花学院科研项目(bkqj2019050)。

摘　　要：利用时域微分求积法和非等距网格,构造了一类A(α)-稳定或有限区间稳定的线性多步法.根据Dahlquist等价性定理,新的线性多步公式是收敛的.理论证明了新的隐式线性多步法公式是A(α)-稳定的或有限区间稳定的.通过数值实验的对比,表明了新的线性多步法比现有的线性多步法具有更好的数值性能.In this paper,a time domain differential quadrature method and non-equidistant grids are used to construct a class of A(α)-stable or finite interval stability linear multistep methods.According to Dahlquist’s equivalence theorem,the new linear multistep formulas are convergent.The theory proves that the new implicit linear multistep method formula is A(α)-stability or finite interval stability.The comparison of numerical experiments shows that the new linear multistep method has better numerical performance than the existing linear multistep method.

关 键 词：线性多步法 微分求积法 非等距网格 数值实验 

分 类 号：O241.8[理学—计算数学]