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   Two New Three and Four Parametric With Memory Methods For Solving Nonlinear ‎Equations‎  
نویسنده Lotfi T. ,‎Assari‎ P.
منبع International Journal Of Industrial Mathematics - 2015 - دوره : 7 - شماره : 3 - صفحه:269 -276
چکیده    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.
کلیدواژه Nonlinear Equation ,With Memory Method ,R-Order Of Convergence ,Self Accelerating Parameter ,Efficiency ‎Index
آدرس Department Of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, ‎Iran‎, ایران, Department Of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, ‎Iran‎, ایران

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