Abstract
In a previous paper it was shown that for a class of semi-linear problems many high order Runge-Kutta methods have order of optimalB-convergence one higher than the stage order. In this paper we show that for the more general class of nonlinear dissipative problems such as result holds only for a small class of Runge-Kutta methods and that such methods have at most classical order 3.
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Burrage, K., Hundsdorfer, W.H. The order ofB-convergence of algebraically stable Runge-Kutta methods. BIT 27, 62–71 (1987). https://doi.org/10.1007/BF01937355
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DOI: https://doi.org/10.1007/BF01937355