عنوان المقالة: One dimensional nonlinear integral operator with Newton–Kantorovich method
د.حميد حسام حميد | Hameed Husam Hameed | 5719
نوع النشر
مجلة علمية
المؤلفون بالعربي
حميد حسام حميد
المؤلفون بالإنجليزي
Z.K. Eshkuvatov , Hameed Husam Hameed , N.M.A. Nik Long
الملخص الانجليزي
The Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have applied NKM to Volterra-type nonlinear integral equations then the method of Nystrom type Gauss–Legendre quadrature formula (QF) was used to find the approximate solution of a linear Fredholm integral equation. New concept of determining the solution based on sub collocation points is proposed. The existence and uniqueness of the approximated method are proven. In addition, the convergence rate is established in Banach space. Finally illustrative examples are provided to validate the accuracy of the presented method
تاريخ النشر
17/06/2016
الناشر
Journal of King Saud University –Science
رقم المجلد
28
رقم العدد
2
ISSN/ISBN
1018-3647
رابط DOI
https://doi.org/10.1016/j.jksus.2015.10.004
الصفحات
172-177
رابط الملف
تحميل (142 مرات التحميل)
رابط خارجي
https://www.sciencedirect.com/science/article/pii/S101836471500097X
الكلمات المفتاحية
Newton–Kantorovich method; Nonlinear operator; Volterra integral equation; Gauss–Legendre quadrature
رجوع