A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational ...

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...

2 School of Mathematics The University of New South Wales, Sydney NSW 2052, Australia Abstract:We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results ar...

The existence of solutions for singular higher order differential equations with the Lidstone or the (n, p) boundary conditions is proved. The righthand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities. Proofs are based on the method of a priori estim...

In this work, we are concerned with a boundary value problem associated with a generalized Fisher-like equation. This equation involves an eigenvalue and a parameter which may be viewed as a wave speed. According to the behavior of the nonlinear source term, existence results of bounded solutions, positive solutions, classical as well as weak solutions are provided. We mainly use fixed point ar...

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...