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Analysis of stepsize selection schemes for Runge-Kutta codes

Hall, G. and Higham, D.J. (1988) Analysis of stepsize selection schemes for Runge-Kutta codes. IMA Journal of Numerical Analysis, 8 (3). pp. 305-310. ISSN 0272-4979

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Conditions on Runge-Kutta algorithms can be obtained which ensure smooth stepsize selection when stability of the algorithm is restricting the stepsize. Some recently derived results are shown to hold for a more general test problem.