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Received August 6, 2022; Accepted October 31, 2022; Published February 20, 2023
Abstract. Several methods are used to develop iterative schemes for solving equations. Higher-order derivatives, on the other hand, are often considered to be used in the calculation of convergence order. But the derivatives are not on the schemes. More significantly, there are no bounds on the error and uniqueness information for the solution to be generated either. So the advantages of these algorithms are restricted in their use of equations with operators that are at least seven times differentiable. We investigate the ball of convergence analysis using only the first derivative for two sixth-order algorithms that are run under an equal set of circumstances. In addition, we provide a calculable ball comparison between the two schemes under consideration. Our technique is based on the first derivative that only appears on the schemes. This way, we can make these schemes more useful for addressing equations involving Banach space-valued operators. Hence, the applicability is extended for these schemes. The technique can be used on other schemes.
How to Cite this Article:
I.K. Argyros, S. Regmi, C.I. Argyros, D. Sharma, Extended efficient high convergence order schemes for equations, Commun. Optim. Theory 2023 (2023) 7.