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

Document Type : Research Article

Authors

• P. Rahimkhani ¹
• R. Moeti ²

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

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

10.22067/ijnao.2024.88927.1479

Abstract

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.

Keywords

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

Main Subjects

• Computational Mathematics

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