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PreprintCC BY 4.0arXiv

Analytical Methods for Solving Non-Autonomous Higher-Order Nonlinear Difference Equations

  • Tshifhiwa Murovhi
  • Mensah Folly-Gbetoula
  • Kwassi Anani
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Abstract

A system of four-dimensional fifth-order rational difference equations with variable coefficients is considered. The method employed is the well-known Lie symmetry analysis initially developed for differential equations. Linearised symmetry conditions are applied, reduction operators are introduced, functional equations are solved, and symmetry generators are derived. The admitted point symmetries are then used to construct closed-form solutions. This work is a non-autonomous generalisation of autonomous fifth-order rational systems in the literature.

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Cite

BibTeXRIS
BibTeX
@misc{murovhi2026analytical,
  title = {{Analytical Methods for Solving Non-Autonomous Higher-Order Nonlinear Difference Equations}},
  author = {Tshifhiwa Murovhi and Mensah Folly-Gbetoula and Kwassi Anani},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24657},
  eprint = {2610.24657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24657},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Analytical Methods for Solving Non-Autonomous Higher-Order Nonlinear Difference Equations
AU  - Tshifhiwa Murovhi
AU  - Mensah Folly-Gbetoula
AU  - Kwassi Anani
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24657
UR  - https://arxiv.org/abs/2610.24657
AB  - A system of four-dimensional fifth-order rational difference equations with variable coefficients is considered. The method employed is the well-known Lie symmetry analysis initially developed for differential equations. Linearised symmetry conditions are applied, reduction operators are introduced, functional equations are solved, and symmetry generators are derived. The admitted point symmetries are then used to construct closed-form solutions. This work is a non-autonomous generalisation of autonomous fifth-order rational systems in the literature.
ER  -