Purpose – The aim of this research is to find accurate solution for the Troesch’s problem by using high
performance technique based on parallel processing implementation.
Design/methodology/approach – Feed forward neural network is designed to solve important type of differential equations that arises in many applied sciences and engineering applications. The suitable designed based on choosing suitable learning rate, transfer function, and training algorithm. The authors used back propagation with new implement of Levenberg - Marquardt training algorithm. Also, the authors depend new idea for choosing the weights. The effectiveness of the suggested design for the network is shown by using it for solving Troesch problem in many cases.
Findings – New idea for choosing the weights of the neural network, new implement of Levenberg - Marquardt training algorithm which assist to speeding the convergence and the implementation of the suggested design demonstrates the usefulness in finding exact solutions.
Practical implications – The authors have applied the suggested design of feed forward neural network to solve Troesch’s problem which is an important equation in Magnetostatic Fields, Electrochemical, a Magnetic Field and others. Originality/value – In this paper, main types of the differential equation have been solved by using parallel processing technique based on feed forward neural network.
The design has been accompanied with new implementation of training algorithm. This process constructs an efficient dealing to get the exact solutions of the non-linear problems which is easy to implement.
In addition to that, the accompanied regularization design with the used design proved its efficiency in handling many problems especially ill-posed problems.
تاريخ النشر
20/01/2019
الناشر
Sci.Int.(Lahore)
رقم المجلد
31
رقم العدد
1
ISSN/ISBN
1013-5316
الصفحات
41-48
الكلمات المفتاحية
Ordinary Differential Equation, Troesch’s Problem, Feed Forward Neural Network, Back propagation Training Algorithms, Levenberg - Marquardt algorithm.
عثمان مهدي صالح | Othman Mahdi Salih | 1722