A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence

New high-order methods for solving non-linear equations

In this paper, we present two families of third and fourth order iterative methods for solving nonlinear equations. The efficiency index of the proposed schemes is 1.442 and 1.587. In order to compare the performance with some of the existing schemes, several numerical examples are furnished here

Families of Iterative Methods with Higher Convergence Orders for Solving Nonlinear Equations

Recently, there has been progress in developing Newton-type methods with higher convergence to solve nonlinear equations. This paper develops new classes of iterative methods with higher convergence orders (more than four) by a construction of two iterative methods of integer-order of convergence, , and > . The construction of such methods provides new classes of methods of order 2 + of convergence. Numerical examples are provided, as well as the use of other existing methods to demonstrate the performance of the presented methods

Explicit preconditioned domain decomposition schemes for solving nonlinear boundary value problems

AbstractA new class of inner-outer iterative procedures in conjunction with Picard-Newton methods based on explicit preconditioning iterative methods for solving nonlinear systems is presented. Explicit preconditioned iterative schemes, based on the explicit computation of a class of domain decomposition generalized approximate inverse matrix techniques are presented for the efficient solution of nonlinear boundary value problems on multiprocessor systems. Applications of the new composite scheme on characteristic nonlinear boundary value problems are discussed and numerical results are given