Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|m) w.r.t. the maximal step size |h|. This m-TDS represen...

In this paper, a novel method is proposed for solving nonlinear singular fourth order four-point boundary value problems (BVPs) by combining advantages of the homotopy perturbed method (HPM) and the reproducing kernel method (RKM). Some numerical examples are presented to illustrate the strength of the method. © 2011 Elsevier Ltd. All rights reserved.

Recommended by Jean Mawhin This paper is concerned with nonhomogeneous multipoint boundary value problems of second-order differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three solutions may be not positive of these BVPs are established.

In this chapter, non-polynomial spline functions are applied to develop numerical methods for obtaining smooth approximations for the following BVP:     6 , , , / , D y x f x y a x b D d dx     (3.1) subject to the boundary conditions: 2 4 0 2 4 2 4 0 2 4 , , , , ,. y a A D y a A D y a A y b B D y b B D y b B       (3.2) where   y x and (,) f x y are continuous functions defined...

From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1–9, 11–17]). However, for the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. The authors made some attempts to solve the nth-order Robin problem [14]. Now ...

Abstract: This paper deals with existence of solutions to three-point BVPs in perturbed systems of first-order ordinary differential equations at resonance. An existence theorem is established by using the Theorem of Borsuk and some examples are given to illustrate it. A result for computing the local degree of polynomials whose terms of highest order have no common real linear factors is also ...