Reduction of Second-Order Ordinary Differential Equations into General Linear Equations via Point Transformations and its Application

Authors

Supaporn Suksern, Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand\\Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, ThailandFollow
Chanikan Sawatdithep, Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandFollow

Author Country (or Countries)

Thailand

Abstract

We study the linearization of nonlinear second-order ordinary differential equations from the point transformation viewpoint. A new algorithm for finding linearizing point transformation is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is in the general form. The general solution of this class of equations is obtained by solving the linearized equation and applying the point transformation. Moreover, we apply the obtained linearization criteria to the interesting problems of nonlinear ordinary differential equations, nonlinear partial differential equations and system of nonlinear ordinary differential equations.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140209

Recommended Citation

Suksern, Supaporn and Sawatdithep, Chanikan (2020) "Reduction of Second-Order Ordinary Differential Equations into General Linear Equations via Point Transformations and its Application," Applied Mathematics & Information Sciences: Vol. 14: Iss. 2, Article 9.
DOI: http://dx.doi.org/10.18576/amis/140209
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss2/9