gðð yðaÞ; yðs2ðbÞÞ; yðeÞ; ð yDðaÞ; yDðsðbÞÞÞÞ 1⁄4 ð0; 0Þ; a , e , s2ðbÞ; e [ T; ð2Þ where f : 1⁄2a; b £ R! R; g : R £ R £ R ! R are continuous, and t is from a so-called “time scale” T. It is assumed that the reader is familiar with the time scale calculus and associated definitions such as delta derivative, jump operators and right-dense continuity. If not, then we refer the reader to Ref. [2]...

Short review of an approach to explicit solving of initial and boundary value problems (BVPs) for some partial differential equations (PDEs) is presented. A combination of two classical methods Å the Fourier method and the Duhamel principle Å is used in the framework of a two-dimensional operational calculus. It gives explicit solutions of some local and nonlocal BVPs for the classical equation...

In this paper we develop an efficient method based on the Spectral Collocation Method (SCM) and the Variational Iteration Method (VIM) that can be used for the efficient numerical solution of nonlinear stiff/nonstiff two-point Boundary Value Problems (BVPs). The method derived here has the advantage that it does not require the solution of nonlinear systems of equations. We derive the method wh...

In this chapter we discuss discrete variable methods for solving BVPs for ordinary differential equations. These methods produce solutions that are defined on a set of discrete points. Methods of this type are initial-value techniques, i.e., shooting and superposition, and finite difference schemes. We will discuss initialvalue and finite difference methods for linear and nonlinear BVPs, and th...

Abstract This paper is concerned with a class of boundary value problems for the nonlinear impulsive functional integro-differential equations with a parameter by establishing new comparison principles and using the method of upper and lower solutions together with monotone iterative technique. Sufficient conditions are established for the existence of extremal system of solutions for the given...

In recent times, numerical approximation of 3rd-order boundary value problems (BVPs) has attracted great attention due to its wide applications in solving arising from sciences and engineering. Hence, A higher-order block method is constructed for the direct solution linear non-linear BVPs. The approach interpolation collocation adopted derivation. Power series approximate interpolated at point...

The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, ...