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Performance of Genocchi wavelet neural networks and least squares support vector regression for solving different kinds of differential equations

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Abstract

In this study, two numerical methods [(a) artificial neural network method with three layers (input layer, hidden layer, output layer) and (b) least squares support vector regression (LS-SVR) method] are suggested for solving three classes of differential equations. For the first method, we use the Genocchi wavelets, inverse trigonometric functions and hyperbolic functions as activation functions. In the second method, we apply the Genocchi wavelets kernel and the collocation LS-SVR method for training the network. Then, for the two methods, the formulation of the methods gives rise to an optimization problem. Finally, the classical optimization and Newton’s iterative method are applied to train these networks. Also, some useful theorems concerning the error analysis associated with the LS-SVR scheme are proved in our article. Finally, some test problems are included to show the efficiency and accuracy of the current methods.

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Data availability

The datasets generated and analyzed during the current study are not publicly available [because this research is ongoing and we cannot make the data available to the public at this time], but are available from the corresponding author on reasonable request.

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Acknowledgements

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the paper.

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

    Parisa Rahimkhani

  2. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Yadollah Ordokhani

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  1. Parisa Rahimkhani
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  2. Yadollah Ordokhani
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Correspondence to Yadollah Ordokhani.

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Rahimkhani, P., Ordokhani, Y. Performance of Genocchi wavelet neural networks and least squares support vector regression for solving different kinds of differential equations. Comp. Appl. Math. 42, 71 (2023). https://doi.org/10.1007/s40314-023-02220-1

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