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

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Rahimkhani P.; Moeti Reza

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2025 | Volume:15 | Issue:1 Page(s): 375-395

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Information Journal Paper

Title

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

Author(s)

Rahimkhani P. | Moeti Reza | Issue Writer Certificate

Keywords

Morgan-Voyce even Fibonacci polynomials

Neural Network

Lienard' s equation

Numerical Method

Abstract

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.

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