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A note on the continuous-stage Runge–Kutta(–Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)

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  • Amodio, Pierluigi
  • Brugnano, Luigi
  • Iavernaro, Felice

Abstract

In recent years, the class of energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) has been devised for numerically solving Hamiltonian problems. In this short note, we study their natural formulation as continuous-stage Runge–Kutta(–Nyström) methods, which allows a deeper insight in the methods.

Suggested Citation

  • Amodio, Pierluigi & Brugnano, Luigi & Iavernaro, Felice, 2019. "A note on the continuous-stage Runge–Kutta(–Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:35
    DOI: 10.1016/j.amc.2019.124634
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    1. Tang, Wensheng & Sun, Yajuan & Zhang, Jingjing, 2019. "High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 670-679.
    2. Barletti, L. & Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2018. "Energy-conserving methods for the nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 3-18.
    3. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
    4. Tang, Wensheng & Zhang, Jingjing, 2018. "Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 204-219.
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