Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation

Fredrik Johansson; Manuel Kauers; Marc Mezzarobba

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.

Document type :

Conference papers

Domain :

Computer Science [cs] / Symbolic Computation [cs.SC]

Complete list of metadatas

https://hal.inria.fr/hal-00818789
Contributor : Marc Mezzarobba <>
Submitted on : Monday, April 29, 2013 - 10:58:30 AM
Last modification on : Tuesday, June 26, 2018 - 2:42:20 PM

Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation

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Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation

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