On two-step parallel computer algorithm for all nonlinear equations roots with engineering applications

Abstract

In this paper, we develop an optimal family of two-step single root finding methods with order 4.Furthermore, we modify these numerical schemes to locate all nonlinear real and complexroots at the same time. The order of convergence is demonstrated using convergence analysisto be four for a single root-finding technique and for families of parallel computer methods.Numerical test examples reveal that the developed parallel techniques achieve superior stabilityand consistency compared to existing approaches.