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.

EUDML-ID : urn:eudml:doc:287853
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@article{702896,
     title = {The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation},
     booktitle = {Applications of Mathematics 2012},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2012},
     pages = {99-106},
     mrnumber = {MR3204403},
     zbl = {1313.65184},
     url = {http://dml.mathdoc.fr/item/702896}
}

Faragó, István; Havasi, Ágnes; Zlatev, Zahari. The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation, dans Applications of Mathematics 2012, GDML_Books,  (2012), pp. 99-106. http://gdmltest.u-ga.fr/item/702896/