Search of rational solutions to differential and difference systems by means of formal series

Systems of linear ordinary differential and difference equations of arbitrary order with polynomial coefficients are considered. An algorithm for searching their rational solutions is suggested. The algorithm is based on the fact that these solutions are expanded into formal series that become polyn...

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Bibliographic Details
Published in:Programming and computer software 2015-03, Vol.41 (2), p.65-73
Main Author: Abramov, S. A.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Computer programs
Computer Science
Difference equations
Differential equations
Mathematical models
Operating Systems
Polynomials
Programming
Search algorithms
Searching
Software Engineering
Software Engineering/Programming and Operating Systems
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Summary:Systems of linear ordinary differential and difference equations of arbitrary order with polynomial coefficients are considered. An algorithm for searching their rational solutions is suggested. The algorithm is based on the fact that these solutions are expanded into formal series that become polynomials after multiplication by a universal denominator. A combined algorithm relying on heuristics is also described. To reduce the amount of computation, at a certain moment, the latter selects between two algorithms, the new one and the standard algorithm based on the use of the universal denominator for changing unknowns and subsequent search for polynomial solutions.
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768815020024