Symmetric second derivative integration methods

被引：7
|
作者：
Nasab, M. Hosseini [1 ]
Abdi, A. [1 ]
Hojjati, G. [1 ]
机构：
[1] Univ Tabriz, Fac Math Sci, Tabriz, Iran
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 330卷
关键词：
Hamiltonian systems; General linear methods; Second derivative methods; Symmetric methods; G-symplecticity; Reversible problems; GENERAL LINEAR METHODS; RUNGE-KUTTA METHODS; ORDINARY DIFFERENTIAL-EQUATIONS; G-SYMPLECTIC METHODS; MULTISTEP METHODS; NUMERICAL-INTEGRATION; HAMILTONIAN PROBLEMS; STIFF ODES; ORDER; STABILITY;
D O I：
10.1016/j.cam.2017.09.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is the derivation of symmetric second derivative general linear methods (SGLMs) for general time-reversible differential equations. For this purpose, we find algebraic conditions on the coefficients matrices of the methods which are sufficient for the method to be symmetric. Some symmetric methods of order 4 are constructed and implemented on the famous reversible problems. Numerical experiments show that the constructed symmetric SGLMs approximately conserve the invariants of motion over long time intervals for reversible Hamiltonian systems. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：618 / 629
页数：12
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