Numerical simulation of nonlinear Li´enard’s equation via Morgan–Voyce even Fibonacci neural network

Iranian Journal of Numerical Analysis and Optimization

مقاله 14، دوره 15، Issue 1 - شماره پیاپی 32، خرداد 2025، صفحه 375-395   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.88927.1479

نویسندگان

P. Rahimkhani¹؛ R. Moeti^{* 2}

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´enard’s equations. 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 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 an-alyze four examples using graphs and tables to demonstrate the accuracy and effectiveness of the numerical approach.

کلیدواژه‌ها

Morgan–Voyce even Fibonacci polynomials؛ Neural network؛ Li´enard’s equation؛ Numerical method

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