In the last lecture, we were introduced to the Interior Point Method. The simplex method solves linear programming problems (LP) by visiting extreme points (vertices) on the boundary of the feasible set. In contrast, the interior point method is based on algorithms that find an optimal solution while moving in the interior of the feasible set. Intuitively, in each iteration of the interior poin...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

Methods based on boundary integral equations are widely used in the numerical simulation of electromagnetic scattering in the frequency domain. This article examines a particular class of these methods, namely the Galerkin boundary element approach, from a theoretical point of view. Emphasis is put on the fundamental differences between acoustic and electromagnetic scattering. The derivation of...

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...