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.
- Lipschitz condition
- Ordinary differential equations
ASJC Scopus subject areas
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics