Axioms (Apr 2022)

Continuous-Stage Runge–Kutta Approximation to Differential Problems

  • Pierluigi Amodio,
  • Luigi Brugnano,
  • Felice Iavernaro

DOI
https://doi.org/10.3390/axioms11050192
Journal volume & issue
Vol. 11, no. 5
p. 192

Abstract

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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.

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