# nonlinear equation

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## nonlinear equation

[′nän‚lin·ē·ər i′kwā·zhən]
(mathematics)
An equation in variables x1, …, xn , y which cannot be put into the form a1 x1+ ⋯ + an xn = y.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
 Xiangde Guo, Zhezhao Zeng, The Neural-Network Approaches to Solve Nonlinear Equation, Journal Of Computers, 5/3, March 2010
Secant method [1, 2], which uses divided differences instead of the first derivative of the nonlinear operator, is one of the most famous iterative methods for solving the nonlinear equation. Secant method reads as follows:
The analytical surface derivatives resulting from the interpolation process are replaced into the MA equation and the boundary condition at the reflector's edge leads to a system of nonlinear equations. To solve the system, an iterative numerical technique is employed.
Caption: Figure 1: Schematic diagram of a two-dimensional curve C which is defined by a parameterized scalar nonlinear equation E (i.e., C = {E : (U, [lambda]) [member of] [R.sup.2] [right arrow] R | E(U, [lambda]) = 0}) which presents only one critical point ([U.sub.cr], [[lambda].sub.cr]) in four different situations ((a), (b), (c), and (d)).
In this article, optimization problem like (8) is used to deal with one nonlinear equation system.
Kwun, A new second- order iteration method for solving nonlinear equations", Abstr.
The construction of the nonlinear TDFEM formulation will mainly be based on the most widely used numerical method for solving nonlinear equations, the Newton-Raphson method , due to its quadratic local convergence.
Many researchers developed various models [1-10] to investigate this problem, among which the two-layer model is one of the analytical research models and is formulated with highly nonlinear equations set.
In this paper, we explore numerical methods for solving nonlinear equations using MATLAB.
Let one consider x* as a root of nonlinear equation (1) in the domain D and assume that f(x) is sufficiently differentiable in the neighbourhood of the root.
Furthermore, in order to examine the CPU time changes with respect to the size of the network, we made synthetic networks with 10 and 20 nodes by making the nonlinear equation with corresponding number of variables.

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