Local comparison between two-step methods under the same conditions

Abstract

In earlier studies different methods of same convergence order are campared using numerical examples. The drawback of this approach is that, we do not know: if the results of those comparisons are true if the examples change; the largest radii of convergence; error estimates on distance between the iterate and solution, and uniqueness results that are computable. In this paper we campare the ball convergence of two-step iterative methods for solving the equation G(x) = 0 using only the first derivative and a common set of criteria. Numerical experiments are used to test the convergence criteria and further validate the theoretical results. Our technique can be used to make comparisons between other methods of the same order. © 2021, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.