Several two-point with memory iterative methods for solving nonlinear equations

In this article, our main motivation is to present two-step with memory iterative methods for solving nonlinear equations. We attempted to convert the existing fourth-order without memory method into a with memory method. Further acceleration of convergence order is attained by means of different ap...

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Bibliographic Details
Published in:Afrika mathematica 2018-06, Vol.29 (3-4), p.435-449
Main Authors: Choubey, Neha, Panday, Bhavna, Jaiswal, J. P.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computing time
Convergence
Hermite polynomials
History of Mathematical Sciences
Iterative methods
Mathematics
Mathematics and Statistics
Mathematics Education
Methods
Nonlinear equations
Parameters
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Summary:In this article, our main motivation is to present two-step with memory iterative methods for solving nonlinear equations. We attempted to convert the existing fourth-order without memory method into a with memory method. Further acceleration of convergence order is attained by means of different approximations of self-accelerating parameters. The parameters are calculated by Hermite interpolating polynomial and applied to accelerate the order of convergence of the without memory methods. In particular, the R -order of the proposed two-step with memory iterative method is increased without any additional calculations and it possesses high computational efficiency. At the end, the theoretical results are confirmed by considering different numerical examples. Numerical comparisons specify that the new family is efficient and give tough competition to some existing with memory iterative methods.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-018-0552-x