We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

In atmospheric dynamics, the governing equations are usually non-linear partial differential equations. Some knowledge of finite-difference approximations to ordinary differential equations (especially first order) is needed, however. In fact, if we linearize a governing partial differential equation and assume a wave form for the solution, the equation simply reduces to an ordinary differentia...

We study the implicit second order ordinary differential equations with complete integral. In this paper, we give a characterization of the implicit second order ordinary differential equations with smooth complete integral which we call Clairaut type equations. Besides, we consider properties of the Clairaut type equations and present the duality among special completely integrable equations w...

The belonging of solutions to a certain function space is a characteristic property for studying the asymptotic behavior of solutions of differential equations. Many works are concerned with the connection between the properties of solutions and stability. We name here the monographs [1-3] on ordinary differential equations and the works [4-9] on functional differential equations. For different...