Differential inequalities for functional perturbations of first-order ordinary differential equations

Differential inequalities for functional perturbations of first-order ordinary differential equations

The theory of differential inequalities plays a central role in the qualitative and quantitative study of differential equations. In this paper, we present several comparison results for a class of functional differential equations of first order with periodic boundary value conditions. The inequalities obtained are, generally speaking, of the following type: Pv 5 0 implies that v 5 0, where P ...

Order Ordinary Differential Equations

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

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...

The Functional Formulation of Second-order Ordinary Differential Equations

In this paper, the necessary and sufficient conditions in order that a smooth mapping F (τ, α, β, a, b) be a dependence of a complete solution x(τ ) of some second-order ordinary differential equation on Neumann conditions x(α) = a, x(β) = b, α 6= β are deduced. These necessary and sufficient conditions consist of functional equations for F and of a smooth extensibility condition. Illustrative ...

Existence Theorem for First Order Ordinary Functional Differential Equations with Periodic Boundary Conditions