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Multi-point Taylor series to solve differential equations

Abstract : The use of Taylor series is an effective numerical method to solve ordinary differential equations but this fails when the sought function is not analytic or when it has singularities close to the domain. These drawbacks can be partially removed by considering multi-point Taylor series, but up to now there are only few applications of the latter method in the literature and not for problems with very localized solutions. In this respect, a new numerical procedure is presented that works for an arbitrary cloud of expansion points and it is assessed from several numerical experiments. © 2019 American Institute of Mathematical Sciences.
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Submitted on : Sunday, June 6, 2021 - 5:47:40 PM
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Djédjé Sylvain Zézé, Michel Potier-Ferry, Yannick Tampango. Multi-point Taylor series to solve differential equations. Discrete and Continuous Dynamical Systems - Series S, 2019, 12 (6), pp.1791-1806. ⟨10.3934/dcdss.2019118⟩. ⟨hal-03251204⟩



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