Generalized Newton Raphsons method free from second derivative

Volume 9, Issue 5, pp 2823--2831 http://dx.doi.org/10.22436/jnsa.009.05.77

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Authors

Waqas Nazeer - Division of Science and Technology, University of Education, Lahore 54000, Pakistan. Amir Naseem - Department of Mathematics, Lahore Leads University, Lahore 54810, Pakistan. Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, South Korea. Young Chel Kwun - Department of Mathematics, Dong-A University, Busan 49315, South Korea.

Abstract

In this paper, we suggest and analyze two new iterative methods for solving nonlinear scalar equations namely: the modified generalized Newton Raphson's method and generalized Newton Raphson's method free from second derivative are having convergence of order six and five respectively. We also give several examples to illustrate the efficiency of these methods.

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Keywords

• Nonlinear equations
• Newton's method
• generalized Newton Raphson's method
• Halley's method

MSC

•  65H05

References

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