An algorithm for finding all polynomial solutions of nonlinear difference equations

YU Jiangtao; LIU Yinping

doi:10.3969/j.issn.1000-5641.201811037

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YU Jiangtao, LIU Yinping. An algorithm for finding all polynomial solutions of nonlinear difference equations[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 24-39. doi: 10.3969/j.issn.1000-5641.201811037

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YU Jiangtao, LIU Yinping. An algorithm for finding all polynomial solutions of nonlinear difference equations[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 24-39. doi: 10.3969/j.issn.1000-5641.201811037

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An algorithm for finding all polynomial solutions of nonlinear difference equations

doi: 10.3969/j.issn.1000-5641.201811037

YU Jiangtao,
LIU Yinping^,

Department of Computer Science and Technology, East China Normal University, Shanghai　200062, China

More Information

Corresponding author: ypliu@cs.ecnu.edu.cn
Received Date: 2018-09-19
Available Online: 2019-12-26
Publish Date: 2020-01-01

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.
- nonlinear difference equation,
- polynomial solution,
- homogeneous balance principle,
- n-order expansion method

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References

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