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Article

Faragó, István ; Havasi, Ágnes ; Zlatev, Zahari
The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 99-106
MSC: 34A34, 65L05, 65L06, 65L20 | MR 3204403 | Zbl 1313.65184
Keywords:
system of ordinary differential equations; initial value problem; explicit Runge-Kutta method; Richardson extrapolation; convergence acceleration
Summary:
Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.
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