An efficient fourth order weighted-Newton method for systems of nonlinear equations

Authors:
Janak Raj Sharma;Rangan Kumar Guha;Rajni Sharma
Affiliations:
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, India 148106;Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, India 148106;Department of Applied Sciences, D.A.V. Institute of Engineering and Technology, Kabirnagar, India 144008
Venue:
Numerical Algorithms
Year:
2013

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Abstract

In this paper, we develop a fourth order method for solving the systems of nonlinear equations. The algorithm is composed of two weighted-Newton steps and requires the information of one function and two first Fréchet derivatives. Therefore, for a system of n equations, per iteration it uses n驴+驴2n 2 evaluations. Computational efficiency is compared with Newton's method and some other recently published methods. Numerical tests are performed, which confirm the theoretical results. From the comparison with known methods it is observed that present method shows good stability and robustness.