Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

Remus-Daniel Ene () and Nicolina Pop
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Remus-Daniel Ene: Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania
Nicolina Pop: Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 300223 Timisoara, Romania

Mathematics, 2023, vol. 11, issue 23, 1-26

Abstract: The goal of this paper is to build some approximate closed-form solutions for a class of dynamical systems involving a Hamilton–Poisson part. The chaotic behaviors are neglected. These solutions are obtained by means of a new version of the optimal parametric iteration method (OPIM), namely, the modified optimal parametric iteration method (mOPIM). The effect of the physical parameters is investigated. The Hamilton–Poisson part of the dynamical systems is reduced to a second-order nonlinear differential equation, which is analytically solved by the mOPIM procedure. A comparison between the approximate analytical solution obtained with mOPIM, the analytical solution obtained with the iterative method, and the corresponding numerical solution is presented. The mOPIM technique has more advantages, such as the convergence control (in the sense that the residual functions are smaller than 1), the efficiency, the writing of the solutions in an effective form, and the nonexistence of small parameters. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations. The same procedure could be successfully applied to more dynamical systems.

Keywords: modified optimal parametric iteration method; periodical orbits; dynamical system; Hamilton–Poisson realization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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