a new approach utilizing newton method and homotopy analysis method (ham) is proposed for solving nonlinear system of equations. accelerating the rate of convergence of ham, and obtaining a global quadratic rate of convergence are the main purposes of this approach. the numerical results demonstrate the efficiency and the performance of proposed approach. the comparison with conventional homoto...

This document proposes a Newton step graph-based model for Quadratic separable Problems (QSP). The Newton step is well suited for this kind of problems, but when the problem size grows the matrix-based QSP model will grow in a non linear manner. Furthermore, handling the constraints becomes the main problem as we have to select the right constraints in the different solution steps. When this ha...

In this paper we present a unigrid multi–model formulation for transonic flow calculations based on solving, in sequence, the full potential equation and the the Euler equations. The goal is to minimize the overall computation time to simulate steady flows by using a more computational efficient physical model in the early iteration steps. The proposed method is based on two steps. In the first...

In this paper we investigate the solving of conditional models using the boundary crossing algorithm proposed by Zaher (1995). He proposed this algorithm as an alternative to using MINLP techniques for solving. This algorithm involves the execution of several well differentiated activities including logical analysis and continuous reconfiguration of the equations constituting the problem, calcu...

In this paper, we present a full Newton step feasible interior-pointmethod for circular cone optimization by using Euclidean Jordanalgebra. The search direction is based on the Nesterov-Todd scalingscheme, and only full-Newton step is used at each iteration.Furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

In [4] the second author presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(n...

In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations in combination with ad hoc preconditioning tech...

Getting a perfectly centered initial point for feasible path-following interior-point algorithms is hard practical task. Therefore, it worth to analyze other cases when the starting not necessarily centered. In this paper, we propose short-step weighted-path following algorithm (IPA) solving convex quadratic optimization (CQO). The latter based on modified search direction which obtained by tec...

Driven cavity ows by eecient numerical techniques, J. An error estimate for the modiied newton method with applications to the solution of nonlinear two-point boundary value problems, Accurate and economical solution of the pressure head form of Richards' equation by the method of lines, Tech. Application of Newton-Krylov methodology to a three-dimensional unstructured Euler code. and the conce...

Abstract The paper considers the way of reducing time consumed to solve SLAEs with iterative methods by reusing data structures obtained in solution a previous SLAE, or selecting preconditioner from available set preconditioners minimize solving next SLAEs. Such adaptive preconditioning is used time-dependent nonlinear problems. generated at Newton iteration n-1 every computation step are solve...