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Partitioned second derivative methods for separable Hamiltonian problems

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Abstract

In this paper, the partitioned second derivative general linear methods for solving separable Hamiltonian problems are derived which are G-symplectic, interchange symmetry and have zero parasitic growth factors. Order conditions for such methods based on the theory of rooted trees are provided and examples of partitioned pairs of order 2 and 3 are given. The experiments have been performed on some separable problems and no drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals. Also, the results of numerical experiments demonstrate the efficiency of our new methods in comparison with some symplectic and G-symplectic methods.

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Acknowledgements

This research was supported in part by Iran National Science Foundation (INSF) (Grant No. 96011504). The author is grateful to her postdoctoral supervisor, Professor Seyed Mohammad Hosseini of Applied Maths. Dept., for his patient guidance and helpful discussions which have led to this joint work. I also like to thank the editor and anonymous reviewers for their comments that have improved the paper.

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  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat modares University, Tehran, Iran

    Masoumeh Hosseini Nasab

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Nasab, M.H. Partitioned second derivative methods for separable Hamiltonian problems. J. Appl. Math. Comput. 65, 831–859 (2021). https://doi.org/10.1007/s12190-020-01417-5

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