The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis the problem under consideration within closed bounded sets. We develop sufficient conditions which associated mappings will be contractive invariant these sets, generates advances concerning existence, uniqueness approxima...

*Correspondence: [email protected] Institute of Applied Physics and Computational Mathematics, Beijing, 100088, P.R. China College of Mathematics, Jilin University, Changchun, 130012, P.R. China Abstract In this paper, we establish the Nagumo theorems for boundary value problems associated with a class of third-order singular nonlinear equations: (p(t)x′)′′ = f (t, x,p(t)x′, (p(t)x′)′), ∀t ...

We develop a two stage numerical method for computing approximate solutions of a system of third-order boundary value problems associated with odd order obstacle problems. Such a problem arise in physical oceanography and can be studied in the framework of variational inequality theory. We show that the present method is of order two and gives numerical results which are better than the other a...

In this paper concerns the third-order boundary-value problem u′′′(t) + f(t, u(t), u′(t), u′′(t)) = 0, 0 < t < 1, r1u(0)− r2u(0) = r3u(1) + r4u(1) = u′′(0) = 0. By placing certain restrictions on the nonlinear term f , we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The constructio...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

In this article, we present a novel second order numerical method for solving third order boundary value problems using the quartic polynomial splines. We establish the convergence of the method. We present numerical experiments to demonstrate the efficiency of the method and validity of our second order method, which shows that present method gives better results.

Abstract For nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified conditions. We construct a shape function (BSF), is designed conditions and can be employed new by assigning different roles of free in BSF. In first algorithm, let functions complete BSFs bases solution, not only automatically, bu...

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...