Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation

Fredrik Johansson 1 Manuel Kauers 1 Marc Mezzarobba 2, 3
1 RISC - Research Institute for Symbolic Computation
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
3 LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting formal series solutions at the singular points as analytic functions and evaluating them numerically at some common ordinary point. The numerical data is used to determine a small number of combinations of the formal series that may give rise to hyperexponential solutions.
Type de document :
Communication dans un congrès
ISSAC - 28th International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, Massachusetts, United States. ACM, pp.211­­-218, 2013, 〈10.1145/2465506.2465513〉
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https://hal.inria.fr/hal-00818789
Contributeur : Marc Mezzarobba <>
Soumis le : lundi 29 avril 2013 - 10:58:30
Dernière modification le : mardi 26 juin 2018 - 14:42:20

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Fredrik Johansson, Manuel Kauers, Marc Mezzarobba. Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation. ISSAC - 28th International Symposium on Symbolic and Algebraic Computation, Jun 2013, Boston, Massachusetts, United States. ACM, pp.211­­-218, 2013, 〈10.1145/2465506.2465513〉. 〈hal-00818789〉

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