Korean J. Math. Vol. 27 No. 4 (2019) pp.1005-1025
DOI: https://doi.org/10.11568/kjm.2019.27.4.1005

Convergence of a continuation method under majorant conditions}

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Published: Dec 30, 2019
Keywords:
Continuation method, Majorant conditions, Kantorovich-type convergence criterion, Smale-type convergence criterion
Mathematics Subject Classification:
65D10, 65G99, 65K10, 47H17, 49M15

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Shwet Nisha
Department of Mathematics Central University of Jharkhand Brambe Ranchi-835205, India
P. K. Parida
Department of Mathematics Central University of Jharkhand Brambe Ranchi-835205, India
Chandni Kumari
Department of Mathematics Central University of Jharkhand Brambe Ranchi-835205, India

Abstract

The paper is devoted to study local convergence of a continuation method under the assumption of majorant conditions. The method is used to approximate a zero of an operator in Banach space and is of third order. It is seen that the famous Kantorovich-type and Smale-type conditions are special cases of our majorant conditions. This infers that our result is a generalized one in comparison to results based on Kantorovich-type and Smale-type conditions. Finally a number of numerical examples have been computed to show applicability of the convergence analysis.


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Supporting Agencies

This work was supported by Central University of Jharkhand.

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