A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on R are studied. These equations constitute gradient flows for the perturbed information functionals Fα,λ(u) = 1 2α Z

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

On a Class of Fourth-order Nonlinear Difference Equations

We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the...

A general fourth-order family of methods for solving nonlinear equations

In this paper a new family of methods free from second derivative is presented. This new family of methods is constructed such that convergence is of order four. This new iterative family may be views as a extension of King’s family-which is one of the most well-known methods for solving nonlinear equations-furthermore this proposed family contains several existing methods as its particular cas...