A Note on the Integration of Scalar Fourth-Order Ordinary Differential Equations with Four-Dimensional Symmetry Algebras

A Note on Four-Dimensional Symmetry Algebras and Fourth-Order Ordinary Differential Equations

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

Solvability of a Four-point Boundary-value Problem for Fourth-order Ordinary Differential Equations

In this paper we investigate the existence of solutions of a class of four-point boundary-value problems for fourth-order ordinary differential equations. Our analysis relies on a fixed point theorem due to Krasnoselskii and Zabreiko.

Linearization of fourth-order ordinary differential equations by point transformations

We present here the solution of the problem on linearization of fourthorder equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of equations which is linear in the third-order derivative. We provide the linearization test and describe the procedure for obtaining the linearizing transformat...

Conditional Linearizability Criteria for Scalar Fourth Order Semi-Linear Ordinary Differential Equations

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not bee...