

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) 19501956], we develop two new iterative with memory methods for solving a nonlinear equation. the first has two steps with three selfaccelerating parameters, and the second has three steps with four selfaccelerating 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 selfaccelerating parameters are computed applying newton's interpolatory polynomials. moreover, they use three and four functional evaluations per iteration and corresponding rorders 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 ,ROrder 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














Authors















