On the Reduction Process of Nucci-Reduce Algorithm for Computing Nonlocal Symmetries of Dynamical Systems:A case study of the Kepler and Kepler-related problems

TL;DR

This paper improves the Nucci-Reduce algorithm for computing nonlocal symmetries in dynamical systems by introducing an isomorphic transformation that simplifies the reduction process and avoids infinite loops.

Contribution

It presents a novel isomorphic transformation that enhances the Nucci-Reduce algorithm, making the process more efficient and reliable for systems like Kepler's problem.

Findings

The transformation reduces computational efforts.

It prevents infinite loops caused by improper variable choices.

Equivalent systems are easier to solve with Lie symmetry methods.

Abstract

The snags in Nucci(1996)REDUCE algorithm are the intrinsic computational efforts and the ability to recognize the ignorable variable(s) during the reduction process of the algorithm. An inappropriate choice of the ignorable variable(s)may lead to an infinite loop. We construct an isomorphic transformation which ameliorates these problems, and with which a simple, definite steps of algebraic process, produced equivalent system of equations to that of Nucci that are easily solved by Lie point symmetry algorithm.