Work

The Symmetry-Preserving Rosenbrock Approach: Application to Solve the Chaotic Lorenz System

Year: 2025

Type: article

Abstract: This extensive study introduces the Rosenbrock method (RosM) for numerically integrating the chaotic Lorenz system, with a focus on its ability to preserve the system’s intrinsic dynamical and structural symmetries. The Lorenz system exhibits significant symmetry, most notably an inversion symmetry (x,y,z)⟶(−x,−y,z), which is a fundamental feature of its chaotic attractor. We lay forth the algorithm and, after systematic comparisons to explicit Runge–Kutta higher-order schemes and semi-analytically obtained solutions, show that the second-order Rosenbrock method performs with excellent accuracy and stability. Crucially, we demonstrate that RosM reliably preserves the system’s symmetry over long-term integration, a property where some explicit methods can exhibit subtle drift. We give a formal error characterization, assess the computational efficiency, and verify the method via bifurcation analysis to support that RosM is a robust and symmetry-aware tool for simulating chaotic systems.

Source: Symmetry

DOI: 10.3390/sym17111844

Authors: Lakhlifa Sadek, Ibtisam Aldawish

Institutions: Saveetha University, Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University