Explicit Symplectic Runge-Kutta-Nystrom Methods Based on Roots of Shifted Legendre Polynomial

被引：0

作者：

Zhang, Jun ^{[1
]}

Zhang, Jingjing ^{[1
]}

Zhang, Shangyou ^{[2
]}

机构：

[1] East China Jiaotong Univ, Sch Sci, Nanchang 330013, Peoples R China

[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

MATHEMATICS | 2023年 / 11卷 / 20期

基金：

中国国家自然科学基金;

关键词：

explicit symplectic Runge-Kutta-Nystrom methods; the shifted Legendre polynomials; order conditions; five-stage fourth-order; seven-stage fifth-order;

D O I：

10.3390/math11204291

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

To date, all explicit symplectic Runge-Kutta-Nystrom methods of order five or above are derived by numerical solutions of order condition equations and symplectic condition. In this paper, we derive 124 sets of seven-stage fifth-order explicit symplectic Runge-Kutta-Nystrom methods with closed-form coefficients in the Butcher tableau using the roots of a degree-3 shifted Legendre polynomial. One method is analyzed and its P-stable interval is derived. Numerical tests on the two newly discovered methods are performed, showing their long-time stability and large step size stability over some existing methods.

引用

页数：13

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