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, which is here recalled and revisited for general differential problems.