کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4635892 1340716 2006 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical solution for high order differential equations using a hybrid neural network—Optimization method
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Numerical solution for high order differential equations using a hybrid neural network—Optimization method
چکیده انگلیسی

This paper reports a novel hybrid method based on optimization techniques and neural networks methods for the solution of high order ordinary differential equations. Here neural networks is considered as a part of large field called neural computing or soft computing. This means that we propose a new solution method for the approximated solution of high order ordinary differential equations using innovative mathematical tools and neural-like systems of computation. This hybrid method can result in improved numerical methods for solving initial/boundary value problems, without using preassigned discretisation points. The mixture of feed forward neural networks and optimization techniques, based on Nelder–Mead method is used to introduce the close analytic form of the solution for the differential equation. Excellent test results are obtained for the solution of lower and higher order differential equations. The model finds approximation solution for the differential equation inside and outside the domain of consideration for the close enough neighborhood of initial/boundary points. Numerical examples are described to demonstrate the method.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 183, Issue 1, 1 December 2006, Pages 260–271
نویسندگان
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