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Truncation Bounds for Differentially Finite Series

Abstract : We describe a flexible symbolic-numeric algorithm for computing bounds on the tails of series solutions of linear differential equations with polynomial coefficients. Such bounds are useful in rigorous numerics, in particular in rigorous versions of the Taylor method of numerical integration of ODEs and related algorithms. The focus of this work is on obtaining tight bounds in practice at an acceptable computational cost, even for equations of high order with coefficients of large degree. Our algorithm fully covers the case of generalized series expansions at regular singular points. We provide a complete implementation in SageMath and use it to validate the method in practice.
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Submitted on : Tuesday, June 18, 2019 - 3:51:52 PM
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Marc Mezzarobba. Truncation Bounds for Differentially Finite Series. Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2019, 2, pp.99-148. ⟨10.5802/ahl.17⟩. ⟨hal-01817568v2⟩



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