Nowadays, the precise modeling of a nuclear reactor core is a challenge. This task involves several aspects, from the computational power needed to perform simulations, to the physics and analysis of the outcome. The need to better understand the physical phenomena is critical in order to quantify and qualify nuclear safety parameters. Currently, substantial research has been done in order to o...

Variational inequalities, nonlinear programming, complementarity problems and other problems can be reduced to nonsmooth equations, for which some generalizations of Newton's method are known. The Newton path, as a natural generalization of the Newton direction, was suggested by D. Ralph for enlarging the convergence region (globalization) of Newton-Robinson's method in the nonsmooth case. We i...

We derive a general class of iteration schemes for the incompressible Navier{Stokes equations which contains fully coupled solution techniques as well as operator splitting/projection methods. We combine the advantages of both, namely accuracy/stability and eeciency, and obtain a special form of discrete projection schemes. In combination with a nonlinear iteration of quasi{Newton type one may ...

We will present the Newton-Raphson algorithm, and the secant method. A MATLAB function for the Newton-Raphson method. The function.MATLAB has many tools that make this package well suited for numerical computations. The Newton-Raphson method for systems of nonlinear equations.The Newton-Raphson method, or Newton Method, is a powerful technique. Interesting is Section 3, where the birth of the N...

‎the purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎the results presented in the paper generalize and extend several well-known results in the literature‎.

The augmented Lagrangian method (also called as of multipliers) is an important and powerful optimization for lots smooth or nonsmooth variational problems in modern signal processing, imaging optimal control. However, one usually needs to solve a coupled nonlinear system equations, which very challenging. In this paper, we propose several semismooth Newton methods arising subproblems image res...