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.

Continuous-Stage Runge–Kutta Approximation to Differential Problems / Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro. - In: AXIOMS. - ISSN 2075-1680. - ELETTRONICO. - 11:(2022), pp. 192.1-192.17. [10.3390/axioms11050192]

Continuous-Stage Runge–Kutta Approximation to Differential Problems

Luigi Brugnano
;
2022

Abstract

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.
2022
11
1
17
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1265115
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