Note on a parameter switching method for nonlinear ODEs

TL;DR

This paper introduces a parameter switching algorithm for nonlinear ODEs that approximates solutions through periodic parameter changes, analyzing its convergence, dissipative properties, and dynamical behavior with numerical validation.

Contribution

It provides a theoretical framework for the convergence and dynamical analysis of the parameter switching method applied to nonlinear ODEs, including numerical validation.

Findings

The PS algorithm converges under certain conditions.

Dissipative properties of the system are preserved.

Numerical example demonstrates the method's effectiveness.

Abstract

In this paper we study analytically a parameter switching (PS) algorithm applied to a class of systems of ODE, depending on a single real parameter. The algorithm allows the numerical approximation of any solution of the underlying system by simple periodical switches of the control parameter. Near a general approach of the convergence of the PS algorithm, some dissipative properties are investigated and the dynamical behavior of solutions is investigated with the Lyapunov function method. A numerical example is presented