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Construction of G- or G(ϵ)-symplectic general linear methods

Author

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  • Braś, Michal
  • Izzo, Giuseppe
  • Jackiewicz, Zdzislaw

Abstract

We describe the construction of G- or G(ϵ)-symplectic, and parasitism free or ϵ-parasitism free general linear methods for numerical integration of Hamiltonian systems of differential equations. Examples of such methods are presented up to the order p=4 and stage order q=p−1. Numerical experiments confirm that all methods achieve the expected order of accuracy, and that these methods approximately preserve Hamiltonians as well as quadratic invariants of differential systems.

Suggested Citation

  • Braś, Michal & Izzo, Giuseppe & Jackiewicz, Zdzislaw, 2022. "Construction of G- or G(ϵ)-symplectic general linear methods," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322002788
    DOI: 10.1016/j.amc.2022.127204
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