Abstract We discuss a nonlinear domain-decomposition preconditioning method for fully implicit simulations of multicomponent porous media flow based on the additive Schwarz preconditioned exact Newton (ASPEN). The efficiently accelerates convergence by resolving unbalanced nonlinearities in local stage and long-range interactions global stage. ASPEN can improve robustness significantly reduce n...

Abstract The article proposes the main stages of compiling mathematical models for calculating and analyzing dynamic thermal modes asynchronous motors in systems an automated frequency electric drive are described. application maximum principle Newton-Raphson method is given, as well solution problem using principle, which leads to a doubling number differential equations. Under these condition...

The main purpose of this paper is to find fuzzy root of fuzzy polynomials (if exists) by using Newton-Raphson method. The proposed numerical method has capability to solve fuzzy polynomials as well as algebric ones. For this purpose, by using parametric form of fuzzy coefficients of fuzzy polynomial and Newton-Rphson method we can find its fuzzy roots. Finally, we illustrate our approach by nu...

In this note we consider the continuous Galerkin time-stepping method of arbitrary order as a possible discretization scheme nonlinear initial value problems. addition, develop and generalize well-known existing result for discrete solution by applying general linearizing procedure to including also simplified Newton procedure. particular, presented existence results are implied choosing suffic...

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...

A technique for accelerating global convergence of pseudo-transient continuation Newton methods is proposed based on residual smoothing. The motivated by the effectiveness local nonlinear smoothers at overcoming strong transients. In limit a small pseudo-time step, method reduces to smoothing technique, while in large steps, an exact recovered along with its quadratic properties. formulation re...

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable any line-search method. In particular, we combine Newton-type directions with scaled SD steps have suitable descent directions. Scaling step length makes significant difference respect similar approaches, terms b...

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...