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
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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.File in questo prodotto:
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