This paper is concerned with the existence of mild solutions of some classes of initial value problem for firstand second-order impulsive semilinear functional and neutral functional differential equations. Initially, we will consider initial value problems for firstorder impulsive semilinear functional differential equations y′(t)−Ay(t) = f (t, yt), a.e. t ∈ J := [0,b], t = tk, k = 1, . . . ,m...

Piecewise quasilinearization methods for singular boundary-value problems in second-order ordinary differential equations are presented. These methods result in linear constant-coefficients ordinary differential equations which can be integrated analytically, thus yielding piecewise analytical solutions. The accuracy of the globally smooth piecewise quasilinear method is assessed by comparisons...

A method for solving the inverse variational problem for differential equations admitting a Lie group is presented. The method is used for determining invariant Lagrangians and integration of second-order nonlinear differential equations admitting two-dimensional non-commutative Lie algebras. The method of integration suggested here is quite different from Lie’s classical method of integration ...

This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restrictio...

In this article, we report an implicit rational method for solution of second order initial value problems in ordinary differential equation. We have presented local truncation error and stability property for the proposed method. We observed that the method has cubic rate of convergenceandA-stable. Numerical results for linear and nonlinear problems presented. These results confirm the accurac...