Numerical methods for differential equations
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Abstract
Abstract
In this paper we consider explicit Runge--Kutta (RK) methods for the numerical solution of Initial Value Problems (IVPs) in differential equations in which the last function evaluation in a step is reused, substituting the first evaluation for the next step. This requirement implies that, except for the first step, the computational cost of an $s$--stage explicit RK method reduces from $s$ to $(s-1)$ function evaluations per step. It will be seen that, in general, if a RK method has order $p$, when introducing this reused stage the new method has in general order $
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@article{Calvo2026order,
title = {On the order of Runge Kutta methods reusing last stage},
author = {M. Calvo and Juan I. Montijano and L. Rández},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.06788},
url = {https://doi.org/10.48550/arxiv.2607.06788}
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