Energy-preserving trigonometrically fitted continuous stage Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems

Li, Jiyong; Gao, Yachao

doi:10.1007/s11075-019-00655-4

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2024

Publication Types

Select...

Article5

Book1

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 12 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Continuous-stage Runge-Kutta methods (csRK methods, hereafter), introduced by Butcher [1][2][3], have been used in recent years as a useful tool for studying structurepreserving methods for Hamiltonian problems (see, e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). In particular, we shall at first consider methods, within this latter class, having Butcher tableau in the form:…”

Section: Introductionmentioning

confidence: 99%

Continuous-Stage Runge–Kutta Approximation to Differential Problems

Amodio

Brugnano

Iavernaro

2022

Axioms

View full text Add to dashboard Cite

In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in terms of continuous-stage Runge–Kutta methods. In this review paper, we recall this aspect and extend it to higher-order differential problems.

show abstract