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 ...

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals ...

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 ...

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 ...

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: Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in differential equations. There is a vital role for differential equations in ...

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 ...