Continuous-Stage Runge–Kutta Approximation to Differential Problems

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.

Keywords

• Hamiltonian problems
• Hamiltonian Boundary Value Methods (HBVMs)
• ODE-IVPs
• continuous-stage Runge–Kutta methods
• continuous-stage Runge–Kutta-Nyström methods