Title: Optimised variable step-size algorithm for the solution of dynamical systems

Authors: Joshua Sunday; Richard Olatokunbo Akinola; Joshua Amawa Kwanamu; Dominic Raymond

Addresses: Department of Mathematics, Faculty of Natural Sciences, University of Jos, Nigeria ' Department of Mathematics, Faculty of Natural Sciences, University of Jos, Nigeria ' Department of Mathematics, Faculty of Science, Adamawa State University, Mubi, Nigeria ' Department of Mathematics and Statistics, Faculty of Science, Federal University, Wukari, Nigeria

Abstract: This study focuses on the formulation of optimised variable step-size algorithm (OVSSA) for the solution of dynamical systems. In order to minimise the number of iterations and number of steps taken as well as improve the accuracy of the proposed algorithm, an embedded strategy was deployed in formulating the method using variable stepsize mode. One of the major advantages of the proposed OVSSA is that the algorithm automatically fine-tunes (or adjusts) the stepsize to suit the problem under consideration according to the variable stepsize strategy defined by the authors. Convergence properties of the OVSSA were also analysed theoretically in order to validate its stability and computational reliability. The OVSSA was employed in solving dynamical systems like the Van der Pol, Genesio-Tesi, Kepler and Lorenz systems. The results generated as a result of the application of the OVSSA on dynamical systems clearly showed that the method is convergent and computationally reliable.

Keywords: algorithm; chaos; convergence; dynamical system; fixed stepsize; initial value problem; optimise; stability; stiffness; variable stepsize.

DOI: 10.1504/IJMOR.2025.146357

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.4, pp.470 - 500

Received: 19 Aug 2023
Accepted: 29 Aug 2023
Published online: 27 May 2025 *

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