Many boundary value problems (BVPs) or initial BVPs have non-smooth solutions, with jumps along lower-dimensional interfaces. The Explicit–Jump Immersed Interface Method (EJIIM) was developed following Li’s Fast Iterative IIM (FIIIM), recognizing that the foundation for the efficient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for w...

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...

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...

This paper is concerned with the numerical solution of a system of ordinary di erential equations ODEs y Sy t f t y p on an inter val b subject to boundary conditions g y y b p The ODEs have a coe cient that is singular at t but it is assumed that the boundary value problem BVP has a smooth solution Some popular methods for BVPs evaluate the ODEs at t This paper deals with the practical issues ...

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.

Higher order differential equations have always been a tedious problem to solve for the mathematicians and engineers. Different numerical techniques were carried out to obtain numerical approximations to such problems. This research work presented and illustrated a novel numerical technique to approximate the tenth-order boundary value problems (BVPs). The techniques developed in this research ...

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...

Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to ...