Some higher-order iteration functions for solving nonlinear models

摘要

In this paper, we present a new efficient sixth-order family of Jarratt type methods for solving scalar equations. Then, we extend this family to the multidimensional case preserving the same order of convergence. We also discuss the theoretical convergence properties of the proposed scheme in the case of scalar as well as multidimensional case. The derivation of these schemes are based on weight function approach and free disposable parameters. We also demonstrate the applicability of them on total six number of problems: first five are real life problems namely, continuous stirred tank reactor (CSTR), chemical engineering, the trajectory of an electron in the air gap between two parallel plates, Hammerstein integration and boundary value problems; last one is the standard academic test problem. In addition, numerical comparisons are made to show the performance of the proposed iterative techniques with the existing techniques of the same order in the scalar as well as multi-dimensional case. Finally on the basis of numerical results, we conclude that our techniques perform better in terms of residual error, error between the two consecutive iterations, asymptotic error constant term and approximated root as compared to the existing ones of same order in scalar as well as multidimensional case.