Linearization of coupled second-order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper, we describe ...

Coupled second-order nonlinear differential equations are of fundamental importance in dynamics. In this part of our study on the integrability and linearization of nonlinear ordinary differential ...

In this paper, we propose a method for finding the best piecewise linearization of nonlinear functions. For this aim, we try to obtain the best approximation of a nonlinear function as a piecewise ...

Abstract: Motivated by the mathematics literature on the algebraic properties of so-called “polynomial vector flows”, we propose a technique for approximating nonlinear differential equations by ...

The geometric linearization of nonlinear differential equation is a robust method for the construction of analytic solutions. The method is related to the existence of Lie symmetries which can be used ...

Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey. Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, Samsun, Turkey. In ...

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under ...

Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity ...