-Solution-of-nonlinear-equations.-Bisection-method-bisections-.-Newton-s-method. This code is designed to find roots of functions and visualize the results using both the Bisection and Newton-Raphson ...

Abstract: Systems of nonlinear equations are known as the basis for many models of engineering and data science, and their accurate solutions are very critical in achieving progress in these fields.

In this paper, we propose new variants of Newton’s method based on quadrature formula and power mean for solving nonlinear unconstrained optimization problems. It is proved that the order of ...

Abstract: Many authors suggested methods to solve nonlinear equations. Each of these methods has its advantages and disadvantages. In this work, we chose some methods with low cost and high accuracy ...

The definition of a Taylor polynomial of order k of a function f at a point xo implies that the degree of this polynomial is at most k, but it can be smaller than k (if f (k)(x0) = 0). It is plain to ...

ABSTRACT: This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of ...

SIAM Journal on Numerical Analysis, Vol. 47, No. 3 (2009), pp. 1827-1846 (20 pages) We study the convergence of regularized Newton methods applied to nonlinear operator equations in Hilbert spaces if ...

In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...