A new eight-order symmetric two-step multiderivative method for the numerical solution of second-order IVPs with oscillating solutions

被引：18
|
作者：
Shokri, Ali [1 ]
机构：
[1] Univ Maragheh, Fac Math Sci, Maragheh, Iran
来源：
NUMERICAL ALGORITHMS | 2018年 / 77卷 / 01期
关键词：
Initial value problems; Multiderivative methods; Second-order IVPs; Phase-lag; Ordinary differential equations; Symmetric multistep methods; MINIMAL PHASE-LAG; RUNGE-KUTTA METHODS; HIGH-ORDER METHOD; OBRECHKOFF METHODS; MULTISTEP METHODS; SCHRODINGER-EQUATION; HIGH-EFFICIENT; INTEGRATION; EXPLICIT; FAMILY;
D O I：
10.1007/s11075-017-0306-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce a class of new two-step multiderivative methods for the numerical solution of second-order initial value problems. We generate a two-step, symmetric, multiderivative method of order 8. We also perform a periodicity analysis. In addition, we determine their periodicity regions. Finally, we compare the new methods to the corresponding classical ones and other known methods from the literature, where we show the high efficiency of the new methods.
引用
收藏
页码：95 / 109
页数：15
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