We are presenting a systematic investigation of the implementation of Richardson Extrapolation for two implicit Runge–Kutta methods. Three numerical examples, including an atmospheric chemical scheme used successfully in several extensive environmental studies and described mathematically by a very stiff and badly scaled nonlinear system of ODEs, are presented to illustrate the advantages of the presented approach. The numerical results show that not only are the computations stable, but also the achieved accuracy is higher when the Richardson Extrapolation is additionally applied. It will be possible to derive similar stability and accuracy results for other implicit Runge–Kutta methods.
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