On the design and analysis of high order Weerakoon-Fernando methods based on weight functions

Abstract

In this article, using the idea of weight functions on Weerakoon‐Fernando's method, an optimal fourth‐order method and some higher order multipoint methods for solving nonlinear equations are proposed. These methods are tested in some real applications and numerical examples and the results are compared with some existing methods. Their dynamical behavior on complex polynomials is analyzed and basins of attraction of these methods are presented.