The convergence of diagonally implicit Runge–Kutta methods combined with Richardson extrapolation

Runge–Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool for enhancing the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any of the diagonally implicit (including also the explicit) Runge–Kutta methods with active Richardson extrapolation and show that the numerical solution obtained converges under rather natural conditions.