Abstract. We present a modification of the Lohner algorithm for the computation of rigorous bounds for solutions of ordinary differential equations together with partial derivatives with respect to initial conditions. The modified algorithm requires essentially the same computational effort as the original one. We applied the algorithm to show the existence of several periodic orbits for Rössler equations and the 14-dimensional Galerkin projection of the Kuramoto—Sivashinsky partial differential equation.
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Zgliczynski, P. C1 Lohner Algorithm . Found. Comput. Math. 2, 429–465 (2002). https://doi.org/10.1007/s102080010025
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DOI: https://doi.org/10.1007/s102080010025