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On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

1
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Sangrur 148106, India
2
Department of Physics and Chemistry, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania
*
Authors to whom correspondence should be addressed.
Symmetry 2019, 11(7), 891; https://doi.org/10.3390/sym11070891
Received: 30 May 2019 / Revised: 27 June 2019 / Accepted: 4 July 2019 / Published: 8 July 2019
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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Abstract

We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique. View Full-Text
Keywords: nonlinear equations; systems; derivative-free methods; fast algorithms; computational efficiency nonlinear equations; systems; derivative-free methods; fast algorithms; computational efficiency
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Sharma, J.R.; Kumar, D.; Jäntschi, L. On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems. Symmetry 2019, 11, 891.

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