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

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LOTFI T.; ASSARI P.

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Paper Information

Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2015 | Volume:7 | Issue:3 Page(s): 269-276

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Information Journal Paper

Title

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

Author(s)

LOTFI T. | ASSARI P. | Issue Writer Certificate

Keywords

NONLINEAR EQUATIONQ2

WITH MEMORY METHODQ2

R-ORDER OF CONVERGENCEQ2

SELF ACCELERATING PARAMETERQ2

EFFICIENCY ‎INDEXQ2

Abstract

In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for NONLINEAR EQUATIONs by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative WITH MEMORY METHODs for solving a NONLINEAR EQUATION. The first has two steps with three self-accelerating parameters, and the second has three steps with four self-accelerating parameters. These parameters are calculated using information from the current and previous iteration so that the presented methods may be regarded as the WITH MEMORY METHODs. The self-accelerating parameters are computed applying Newton's interpolatory polynomials. Moreover, they use three and four functional evaluations per iteration and corresponding R-orders of convergence are increased from 4 ad 8 to 7.53 and 15.51, respectively. It means that, without any new function calculations, we can improve convergence order by 93% and 96%. We provide rigorous theories along with some numerical test problems to confirm theoretical results and high computational ‎efficiency.‎

Cites

A NEW ITERATIVE WITH MEMORY CLASS FOR SOLVING NONLINEAR EQUATIONS

References

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APA: Copy

LOTFI, T., & ASSARI, P.. (2015). TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 7(3), 269-276. SID. https://sid.ir/paper/231760/en

Vancouver: Copy

LOTFI T., ASSARI P.. TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2015;7(3):269-276. Available from: https://sid.ir/paper/231760/en

IEEE: Copy

T. LOTFI, and P. ASSARI, “TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 7, no. 3, pp. 269–276, 2015, [Online]. Available: https://sid.ir/paper/231760/en

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