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Paper Information

Journal:   INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS   SUMMER 2015 , Volume 7 , Number 3; Page(s) 269 To 276.
 
Paper: 

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

 
 
Author(s):  LOTFI T.*, ASSARI P.
 
* DEPARTMENT OF MATHEMATICS, HAMEDAN BRANCH, ISLAMIC AZAD UNIVERSITY, HAMEDAN, IRAN
 
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.

 
Keyword(s): NONLINEAR EQUATION, WITH MEMORY METHOD, R-ORDER OF CONVERGENCE, SELF ACCELERATING PARAMETER, EFFICIENCY ‎INDEX
 
 
References: 
 
Citations: 
 
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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. https://www.sid.ir/en/journal/ViewPaper.aspx?id=451817



Vancouver: Copy

LOTFI T., ASSARI P.. TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS. 2015 [cited 2021June21];7(3):269-276. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=451817



IEEE: Copy

LOTFI, T., ASSARI, P., 2015. TWO NEW THREE AND FOUR PARAMETRIC WITH MEMORY METHODS FOR SOLVING NONLINEAR ‎EQUATIONS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, [online] 7(3), pp.269-276. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=451817.



 
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