G-symplectic second derivative general linear methods for Hamiltonian problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:313

Article

Nasab, M. Hosseini¹  Hojjati, G.¹  Abdi, A.¹ 

[1] Univ Tabriz, Fac Math Sci, Tabriz, Iran

关键词: Hamiltonian problems;    General linear methods;    Second derivative methods;    G-symplecticity;    Parasitism;   

DOI  :  10.1016/j.cam.2016.10.011

来源: Elsevier

【 摘 要 】

It is our purpose to design second derivative general linear methods (SGLMs) for solving Hamiltonian problems. To do this, we explore G-symplectic SGLMs which preserve a generalization of quadratic invariants along the long-time integration. We find sufficient conditions on the coefficients matrices of the methods which ensure G-symplecticity and control parasitism. We construct such methods up to order 4. Numerical experiments of the constructed methods on the well-known Hamiltonian problems indicate ability of the methods in solving Hamiltonian problems over long-time integration. (C) 2016 Published by Elsevier B.V.

【 授权许可】

Free