A NEW OPTIMAL METHOD OF FOURTH-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

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LOTFI T.

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Paper Information

Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2014 | Volume:6 | Issue:2 Page(s): 121-124

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Information Journal Paper

Title

A NEW OPTIMAL METHOD OF FOURTH-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Author(s)

LOTFI T. | Issue Writer Certificate

Keywords

NONLINEAR EQUATIONSQ2

MULTI-POINT ITERATIONQ2

KUNG AND TRAUB CONJECTUREQ2

OPTIMAL ORDERQ2

Abstract

In this paper, we present a fourth order method for computing simple roots of NONLINEAR EQUATIONS by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate, namely one evaluation of function and two evaluations of first derivative. So, Kung and Traub's conjecture is fulfilled. We also perform some numerical tests that confirm the theoretical results and allow us to compare the proposed method with some existing methods of the same type.

Cites

TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS

References

OPTIMAL FOURTH ORDER FAMILY OF ITERATIVE METHODS

Cite

APA: Copy

LOTFI, T.. (2014). A NEW OPTIMAL METHOD OF FOURTH-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 6(2), 121-124. SID. https://sid.ir/paper/231809/en

Vancouver: Copy

LOTFI T.. A NEW OPTIMAL METHOD OF FOURTH-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2014;6(2):121-124. Available from: https://sid.ir/paper/231809/en

IEEE: Copy

T. LOTFI, “A NEW OPTIMAL METHOD OF FOURTH-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 6, no. 2, pp. 121–124, 2014, [Online]. Available: https://sid.ir/paper/231809/en

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