In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations the second kind. We construct our new strategy in two steps, through beginning with linearization phase system by applying Newton method, then pass to discretization some involved operator using Nystr\"{o}m method. The convergence analysis method is proved under necessary conditions. At last, ...

An efficient algorithm is described for calculating stationary one-dimensional transonic outflow solutions of the compressible Euler equations with gravity and heat source terms. The stationary equations are solved directly by exploiting their dynamical system form. Transonic expansions are the stable manifolds of saddle-pointtype critical points, and can be obtained efficiently and accurately ...

1 Abstract In this report, we discuss an implementation of a parallel Newton solver for the solution of a structured system of nonlinear equations, F(x) = 0. The evaluation of F(x) and its Jacobian requires evaluating and solving several sparse, banded matrix functions (some symmetric); this makes it possible to use sparse Cholesky routines to dramatically speed up the computation. However, oth...

Partially purified high molecular weight preparations of phytochrome, estimated to be close to 440,000 molecular weight based upon chromatography through a calibrated Bio-Gel P-300 column, were obtained from Garry and Newton oats (Avena Sativa L., cv. Garry and cv. Newton), rye (Secale cereale L., cv. Balbo), barley (Horedum vulgare L., cv. Harrison), and pea (Pisum sativum L., cv. Alaska) by a...

Recurrent Neural Networks (RNNs) are powerful models that achieve unparalleled performance on several pattern recognition problems. However, training of RNNs is a computationally difficult task owing to the well-known “vanishing/exploding” gradient problems. In recent years, several algorithms have been proposed for training RNNs. These algorithms either: exploit no (or limited) curvature infor...

A trust region-based optimization method has been incorporated into the DAKOTA optimization software toolkit. This trust region approach is designed to manage surrogate models of the objective and constraint functions during the optimization process. In this method, the surrogate functions are employed in a sequence of optimization steps, where the original expensive objective and constraint fu...

Abstract—The solution of non linear problems are based on very well grounded mathematical theories. This document proposes a Newton step graph-based model for convex non linear separable problems (NLP) with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLSP model will grow in a non linear manner. Furthermore, the constraints ha...

A new approach based on the use of the Newton and level set methods allows to follow the motion of interfaces with surface tension immersed in an incompressible Newtonian fluid. Our method features the use of a high order fully implicit time integration scheme that circumvents the stability issues related to the explicit discretization of the capillary force when capillary effects dominate. A s...