کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419905 1631779 2016 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A modified iterated projection method adapted to a nonlinear integral equation
ترجمه فارسی عنوان
یک روش پیش بینی اصلاح شده تکرار شده با یک معادله انتگرال غیر خطی سازگار است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی

The classical way to tackle a nonlinear Fredholm integral equation of the second kind is to adapt the discretization scheme from the linear case. The Iterated projection method is a popular method since it shows, in most cases, superconvergence and it is easy to implement. The problem is that the accuracy of the approximation is limited by the mesh size discretization. Better approximations can only be achieved for fine discretizations and the size of the linear system to be solved then becomes very large: its dimension grows up with an order proportional to the square of the mesh size. In order to overcome this difficulty, we propose a novel approach to first linearize the nonlinear equation by a Newton-type method and only then to apply the Iterated projection method to each of the linear equations issued from the Newton method. We prove that, for any value (large enough) of the discretization parameter, the approximation tends to the exact solution when the number of Newton iterations tends to infinity, so that we can attain any desired accuracy. Numerical experiments confirm this theoretical result.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 276, 5 March 2016, Pages 432-441
نویسندگان
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