روش شبکه عصبی موجک‌هان گسسته برای حل عددی معادلات براتو

نویسندگان
پریسا رحیم خانی 1
یدالله اردوخانی 2
1 مرکز آموزش عالی محلات
2 دانشگاه الزهرا
چکیده
در این مقاله یک روش عددی جدید براســاس شــبکه عصــبی و موجکهای هان گســســته برای حل معادلات براتو ارائه میشـود. ابتدا، موجکهای هان گسـسـته و برخی ویژگیهای مهم آن برای سـاختن شـبکه عصـبی موجکهای هان بیان میشـود. شـبکه عصــبی بیان شــده شــامل ســه لایه اســتل لایه ورودی، لایه خروجی و لایه پنهان. در این روش از موجکهای هان و تابع ســینوس هایپربولیک به ترتیب به عنوان توابع فعالســاز لایه پنهان و لایه خروجی اســتداده میشــود. ســپر روش بهینهســازی تحلیلی برای بهدسـت آوردن وزنهای شـبکه عصـبی بهگونهای اسـتداده میشـود که جوا تقریبی در مسـاله قـدن کند. با اسـتداده از این روش، مسـاله اقــلی به یک دســتگاه از معادلات جبری تبدیل میشــود، که این دســتگاه را میتوان با روش تکرار نیوتون حل کرد. در انتها با ارائه مثالهایی دقت و کارائی روش را مورد بررسی قرار میدهیم
کلیدواژه‌ها
شبکه عصبی
موجک‌های هان
معادلات براتو
روش عددی
روش‌های بهینه‌سازی تحلیلی

عنوان مقاله English

A discrete Hahn wavelet neural network method for Bratu-type equations

نویسندگان English

Parisa Rahimkhani 1
Yadollah Ordokhani 2
1 Mahallat Institute of Higher Education
2 Alzahra University
چکیده English

In this paper, a new numerical method based on the neural network and the discrete Hahn wavelets is presented for solving the Bratu-type equations. First, the discrete Hahn wavelets and some of their important properties are expressed to construct the Hahn wavelets neural network. The presented neural network consists of three layers: input layer, hidden layer, output layer. In this method, the Hahn wavelets and sinh functions are used as the activation functions of the hidden layer and output layer, respectively. Then, an analytical optimization method is employed to adjust the neural network weights so that the approximated solution satisfies the given problem. Using this method, the original problem is converted into a system of algebraic equations, which is solved by Newton’s iterative method. Finally, the accuracy and efficiency of the proposed method are examined through several numerical examples.

کلیدواژه‌ها English

Neural Network
Hahn wavelets
Bratu equations
Numerical method
Analytical optimization method
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