کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4631322 | 1340621 | 2012 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Three-point methods with and without memory for solving nonlinear equations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Three-point methods with and without memory for solving nonlinear equations Three-point methods with and without memory for solving nonlinear equations](/preview/png/4631322.png)
چکیده انگلیسی
A new family of three-point derivative free methods for solving nonlinear equations is presented. It is proved that the order of convergence of the basic family without memory is eight requiring four function-evaluations, which means that this family is optimal in the sense of the Kung-Traub conjecture. Further accelerations of convergence speed are attained by suitable variation of a free parameter in each iterative step. This self-accelerating parameter is calculated using information from the current and previous iteration so that the presented methods may be regarded as the methods with memory. The self-correcting parameter is calculated applying the secant-type method in three different ways and Newton's interpolatory polynomial of the second degree. The corresponding R-order of convergence is increased from 8 to 4(1+5/2)â8.472, 9, 10 and 11. The increase of convergence order is attained without any additional function calculations, providing a very high computational efficiency of the proposed methods with memory. Another advantage is a convenient fact that these methods do not use derivatives. Numerical examples and the comparison with existing three-point methods are included to confirm theoretical results and high computational efficiency.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 9, 1 January 2012, Pages 4917-4927
Journal: Applied Mathematics and Computation - Volume 218, Issue 9, 1 January 2012, Pages 4917-4927
نویسندگان
J. DžuniÄ, M.S. PetkoviÄ, L.D. PetkoviÄ,