Construction of Tri-parametric derivative free fourth order with and without memory iterative method

Volume 9, Issue 4, pp 1410--1423 http://dx.doi.org/10.22436/jnsa.009.04.01

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Authors

F. Zafar - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. N. Yasmin - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan. M. A. Kutbi - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia. M. Zeshan - Centre for Advanced Studies in Pure and Applied Mathematics(CASPAM), Bahauddin Zakariya University, Multan 60800, Pakistan.

Abstract

We have given two general methods of converting with derivative two-step methods to without derivative two-step methods. It can also be observed that this conversion not only retain the optimal order of convergence of the two-step methods but the resulting derivative free families of iterative methods are also extendable to with memory class. The with-memory methods show greater acceleration in the order of convergence. In this way, order of convergence is accelerated from 4 to 7.53 at the most. An extensive comparison of our methods is done with the recent methods of respective domain.

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Keywords

• With and without memory methods
• derivative free
• self accelerating parameters
• accelerated order of convergence.

MSC

•  65D05
•  65H05

References

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