Numerical Solution of Nonlinear Equations
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Create Alert. Share This Paper. Tables from this paper. Citations Publications citing this paper. A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations L. Bischof , Ali Bouaricha , Peyvand M. Khademi , Jorge J.
References Publications referenced by this paper. Toint , " Partitioned variable metric updates for large structured optimization problems. Numerical simulations show that the effectiveness and performance of the new method in solving nonlinear equations are encouraging. A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented.
We introduce preconditioners to nonlinear equations or a system of We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method.
The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions. A multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs initial value problems and BVPs boundary value problems is constructed. The multi-step iterative schemes consist of two The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part.
Numerical Methods for Engineers and Scientists 3rd Edition by Amos Gilat
A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. Another new family of Secant-like method is proposed in this paper.
Analysis of convergence shows that the method has a super-linear convergence as Secant method. Numerical experiments show that the efficiency of the method is depended on Numerical experiments show that the efficiency of the method is depended on the value of its parameter. Typically, we are able to solve system of linear or nonlinear equations which are a set of simultaneous equations SE.
Definitely, solving of a linear SE is very easy while we have to use Newton's method to solve nonlinear SEs. The common case for both of them is, to generate an equation for each variable.
It means, we can solve an equation with three variables, if we have three simultaneous equations or solving of four variables needs to find a system of four simultaneous equations and so on. Can we solve a nonlinear equation with many variables? In the special conditions, the answer is positive. The purpose of this article is to present some examples which show us possibility to solve a nonlinear equation with many variables where we have a good estimation for limited domain and range of variables.
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Therefore, this method can be useful for them. On Broyden-like update via some quadratures for solving nonlinear systems of equations. The existing ABS controls have the ability to regulate the level of pressure to optimally The existing ABS controls have the ability to regulate the level of pressure to optimally maintain the wheel slip within the vehicle stability range.
However, the ABS shows strong nonlinear characteristics in which the vehicles equipped with the existing controllers can still have a tendency to oversteer and become unstable. In this paper, a new intelligent robust control method based on an active force control AFC strategy is proposed via a rigorous simulation study.
It is designed and implemented in a hybrid form by having the AFC loop associated with an iterative learning IL algorithm cascaded in series with a self-tuning fuzzy logic FL -based proportional-integral-derivative PID control for the effective overall performance of the proposed ABS. Both the IL and FL techniques are for the appropriate acquisition and computation of the important parameters in the controller.
The incorporation of the AFC-based scheme into the ABS serves to provide an enhanced and robust performance that has the potentials to be implemented in a practical and real-time system.
Chapter 1 - Numerical Solution of Nonlinear Equations.ppt -...
Error Analysis in Iterative Methods. Seminar presentation for Scientific Computing course. This article discusses an iterative method to solve a nonlinear equation, which is free from derivatives by approximating a derivative in the two-step of the method of Xiaojian [Applied Mathematics and Computation, , ] by This article discusses an iterative method to solve a nonlinear equation, which is free from derivatives by approximating a derivative in the two-step of the method of Xiaojian [Applied Mathematics and Computation, , ] by the method of central difference with one parameter.
We show analytically that the method is of order four. Numerical experiments show that the new method is comparable with other discussed method. This article discusses a derivative free iterative method to solve a nonlinear equation.
The method derived by approximating derivatives on a method proposed by Rafiullah [ International Journal of Computer Mathematics, 4: —, The method derived by approximating derivatives on a method proposed by Rafiullah [ International Journal of Computer Mathematics, 4: —, ] using a central difference formula. We show analytically that the method is of an order six. Numerical experiments show that the new method is comparable with other method in terms of the speed in obtaining a root. Leli Deswita. An effective trust-region-based approach for symmetric nonlinear systems.
In this work, we propose a new alternative approximation based on the quasi-Newton approach for solving systems of nonlinear equations using the average of midpoint and Simpson's quadrature. Our goal is to enhance the efficiency of the Our goal is to enhance the efficiency of the method Broyden's method by reducing the number of iterations it takes to reach a solution.
PRECONDITIONING ISSUES IN THE NUMERICAL SOLUTION OF NONLINEAR EQUATIONS AND NONLINEAR LEAST SQUARES
Local convergence analysis and computational results showing the relative efficiency of the proposed method are given. Related Topics. Follow Following. Newton's method. Numerical Optimization.