A GENERAL FAMILY OF DERIVATIVE FREE WITH AND WITHOUT MEMORY ROOT FINDING METHODS | [Journal of Prime Research in Mathematics • 2020]

Author(s):

1. SAIMA AKRAM: Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan

2. FIZA ZAFAR: Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan

3. MOIN-UD-DIN JUNJA: Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan

4. NUSRAT YASMIN: Centre for advanced studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Pakistan

Abstract:

In this manuscript, we construct a general family of optimal derivative free iterative methods by using rational interpolation. This family is further extended to a family of with-memory methods with increased order of convergence by employing two free parameters. At each iterative step, we use a suitable variation of the free parameters. These parameters are computed by using the information from current and previous iterations so that the convergence order of the existing family is increased from 2n to 2n + 2n 1 + 2n 2 without using any additional function evaluations. To check the performance of newly developed iterative schemes with and without memory, an extensive comparison with the existing with- and without memory methods is done by taking some real world problems and standard nonlinear functions. Numerical experiments illustrate that the proposed family of methods with-memory retain better computational e ciency and fast convergence speed as compared to existing with- and without memory methods. The performance of the methods is also analyzed visually by using complex plane. Numerical and dynamical comparisons con rm that the proposed families of with and without memory methods have better e ciency, convergence regions and speed in contrast with the existing methods of the same kind.

Page(s): 64-83

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 16, Issue: 1, Year: 2020

Keywords:

Nonlinear equation , Iterative Methods , polynomiograph

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