کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4631412 1340622 2010 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Derivative free two-point methods with and without memory for solving nonlinear equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Derivative free two-point methods with and without memory for solving nonlinear equations
چکیده انگلیسی

Two families of derivative free two-point iterative methods for solving nonlinear equations are constructed. These methods use a suitable parametric function and an arbitrary real parameter. It is proved that the first family has the convergence order four requiring only three function evaluations per iteration. In this way it is demonstrated that the proposed family without memory supports the Kung–Traub hypothesis (1974) on the upper bound 2n of the order of multipoint methods based on n + 1 function evaluations. Further acceleration of the convergence rate is attained by varying a free parameter from step to step using information available from the previous step. This approach leads to a family of two-step self-accelerating methods with memory whose order of convergence is at least 2+5≈4.236 and even 2+6≈4.449 in special cases. The increase of convergence order is attained without any additional calculations so that the family of methods with memory possesses a very high computational efficiency. Numerical examples are included to demonstrate exceptional convergence speed of the proposed methods using only few function evaluations.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 217, Issue 5, 1 November 2010, Pages 1887–1895
نویسندگان
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