Convergence of Iterative Methods fora Fourth - Order Discretization

On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme

We prove that, under certain conditions, some classical iterative methods converge for the linear system resulting from a fourth-order compact discretization of the convection-diiusion equation.

On Convergence of Iterative Methods for a Fourth-Order Discretization Scheme

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

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.