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 ...

Abstract: Linearization is a powerful tool that enables the analysis and control of nonlinear systems by simplifying their dynamics and allowing the use of well-established linear control techniques.

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

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

Damped Burger’s equation describes the characteristics of one-dimensional nonlinear shock waves in the presence of damping effects and is significant in fluid dynamics, plasma physics, and other ...

Abstract: In this paper, the linearization of a nonlinear vector implicit differential equation that describes mechanical systems with application to robotics is established. In order to come to the ...

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 ...

ABSTRACT: In this paper the Modified Equations of Emden type (MEE), χ+αχχ+βχ 3 is solved numerically by the differential transform method. This technique doesn’t require any discretization, ...