Abstract
Almost Runge–Kutta methods were introduced to obtain many of the advantages of Runge–Kutta methods without their disadvantages. We consider the construction of fourth order methods of this type with a special choice of the free parameters to ensure that, at least for constant stepsize, order 5 behaviour is achieved. It is shown how this can be extended to variable stepsize.
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Butcher, J.C., Moir, N. Experiments with a New Fifth Order Method. Numerical Algorithms 33, 137–151 (2003). https://doi.org/10.1023/A:1025503719518
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DOI: https://doi.org/10.1023/A:1025503719518