A new higher-order optimal derivative free scheme for multiple roots

Abstract

In this paper, we presented a novel and efficient fourth order derivative free optimal family of iterative methods for approximating the multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots afterward it concludes in general form. In addition, we study several numerical experiments on real life problems in order to confirm the efficiency and accuracy of our methods. We illustrate the applicability and comparisons of our methods on eigenvalue problem, Van der Waals equation of state, continuous stirred tank reactor (CSTR), Plank's radiation and clustering problem of roots with earlier robust iterative methods. Finally, on the basis of obtained computational results, we conclude that our methods perform better than the existing ones in terms of CPU timing, absolute residual errors, asymptotic error constants, absolute error difference between two last consecutive iterations and approximated roots compared to the existing ones.