An algorithm for finding all polynomial solutions of nonlinear difference equations

doi:10.3969/j.issn.1000-5641.201811037

Abstract

Abstract: Difference equations are a major aspect of computer algebra; yet, there are currently few studies on solving general nonlinear difference equations. Inspired by the homogeneous balance principle that works well for solving nonlinear differential equations, we use it to find polynomial solutions for a wide range of nonlinear difference equations, in which a new n-order expansion method is proposed to process the powerless cases of the homogeneous balance principle. They are combined together as an algorithm that can be used to find all polynomial solutions of nonlinear difference equations. The algorithm is implemented in Maple, and the experiments show that it is effective and efficient.

Key words: nonlinear difference equation, polynomial solution, homogeneous balance principle, n-order expansion method

CLC Number:

Jiangtao YU, Yinping LIU. An algorithm for finding all polynomial solutions of nonlinear difference equations[J]. Journal of East China Normal University(Natural Science), 2020, 2020(1): 24-39.

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