Abstract
In this paper, we generalize the results of Feng and Gao [Feng, R., Gao, X.S., 2006. A polynomial time algorithm to find rational general solutions of first order autonomous ODEs. J. Symbolic Comput., 41(7), 735–762] to the case of difference equations. We construct two classes of ordinary difference equations ( O Δ Es ) whose solutions are exactly the univariate polynomial and rational functions respectively. On the basis of these O Δ Es and the difference characteristic set method, we give a criterion for an O Δ E with any order and nonconstant coefficients to have a rational type general solution. For the first-order autonomous (constant coefficient) O Δ E , we give a polynomial time algorithm for finding the polynomial solutions and an algorithm for finding the rational solutions for a given degree.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
