Numerical simulation of nonlinear Lienard's equation via Morgan-Voyce even Fibonacci neural network

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 آبان 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.88927.1479

نویسندگان

P. Rahimkhani^{* 1}؛ Reza Moeti²

¹Faculty of Science, Mahallat Institute of Higher Education, Mahallat, Iran

²Department of Mathematics Education, Faculty of Mathematics and Computer, Shahid Bahonar University, Kerman, Iran

چکیده

In the current study, we design a new computational method to solve a class of Li$\acute{e}$nard's equations (LEs). This equation originates from advancements in radio and vacuum tube technology. To attain the proposed goal, we develop a method using a three-layer artificial neural network, consisting of an input layer, a hidden layer, and an output layer. We use the Morgan-Voyce even Fibonacci polynomials (MVEFPs) and $\sinh$ function as activation functions for the hidden layer and the output layer, respectively. Then, the neural network is trained using a classical optimization method. Finally, we analyze four examples using graphs and tables to demonstrate the accuracy and effectiveness of the numerical approach.

کلیدواژه‌ها

Morgan-Voyce even Fibonacci polynomials؛ Neural network؛ Lienard' s equation؛ Numerical method