In this paper, we mainly study the superconvergence properties in approximation of second- and third-order BVPs by spectral collocation methods. The theoretical analyses identify points interpolation function. Ample numerical experiments are carried out which perfectly match results. addition, results show that also hold solving PDEs.

In this paper, by the use of a new fixed point theorem and Green function BVPs, existence at least one positive solution for third-order boundary value problem with integral conditions is considered,where there nonnegative continuous function. Finally, an example which to illustrate main conclusions paper given.

Keywords: Positive solutions Third-order three-point BVPs Nonhomogeneous Fixed point theorem Existence and nonexistence a b s t r a c t In this work, by employing the Guo–Krasnosel'skii fixed point theorem and Schauder's fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary value problem u (t) + a(t)f (u(t)) = 0...

Here, we investigate boundary-value problems (BVPs) for systems of second-order, ordinary, delay-differential equations. We introduce some differential inequalities such that all solutions (and their derivatives) to a certain family of BVPs satisfy some a priori bounds. The results are then applied, in conjunction with topological arguments, to prove the existence of solutions. We then apply ea...

Boundary value problems (BVPs) have been studied for a long period. At the beginning, most researchers focused on two-point BVPs with four classical boundary conditions (BCs) of Dirichlet type u() = u() = , Neumann type u′() = u′() = , Robin type u() = u′() =  or u′() = u() = , and Sturm-Liouville type αu() – βu′() = , γu() + δu′() = . Later, in order to meet the requirements ...

In this paper, the direct three-point block one-step methods are considered for solving linear boundary value problems (BVPs) with two different types of boundary conditions which is the Dirichlet and Neumann boundary conditions. This method will solve the second order linear BVPs directly without reducing it to the system of first order equations. The direct solution of these two types of BVPs...

In this paper, we obtain sufficient conditions for existence of solutions a third order m-point impulsive boundary value problem on time scales. To the best our knowledge, there is hardly any work dealing with multi point dynamic BVPs. The reason may be complex arguments caused by both perturbations and calculations As an application, give example demonstrating results.

This article analyzes the solvability of second-order, nonlinear dynamic boundary value problems (BVPs) on time scales. New Bernstein-Nagumo conditions are developed that guarantee an a priori bound on the delta derivative of potential solutions to the BVPs under consideration. Topological methods are then employed to gain solvability.

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, ...

This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction...