Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model
The motivation behind this study is to simplify the complex mathematical formulations and reduce the time-consuming processes involved in traditional numerical methods for solving differential equations. This study develops a computational intelligence approach with a Morlet wavelet neural network (...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Computers |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-431X/14/1/14 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588801257504768 |
|---|---|
| author | Ali Hasan Ali Muhammad Amir Jamshaid Ul Rahman Ali Raza Ghassan Ezzulddin Arif |
| author_facet | Ali Hasan Ali Muhammad Amir Jamshaid Ul Rahman Ali Raza Ghassan Ezzulddin Arif |
| author_sort | Ali Hasan Ali |
| collection | DOAJ |
| description | The motivation behind this study is to simplify the complex mathematical formulations and reduce the time-consuming processes involved in traditional numerical methods for solving differential equations. This study develops a computational intelligence approach with a Morlet wavelet neural network (MWNN) to solve the nonlinear Van der Pol–Mathieu–Duffing oscillator (Vd-PM-DO), including parameter excitation and dusty plasma studies. The proposed technique utilizes artificial neural networks to model equations and optimize error functions using global search with a genetic algorithm (GA) and fast local convergence with an interior-point algorithm (IPA). We develop an MWNN-based fitness function to predict the dynamic behavior of nonlinear Vd-PM-DO differential equations. Then, we apply a novel hybrid approach combining WCA and ABC to optimize this fitness function, and determine the optimal weight and biases for MWNN. Three different variants of the Vd-PM-DO model were numerically evaluated and compared with the reference solution to demonstrate the correctness of the designed technique. Moreover, statistical analyses using twenty trials were conducted to determine the reliability and accuracy of the suggested MWNN-GA-IPA by utilizing mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and mean square error (MSE). |
| format | Article |
| id | doaj-art-d0efb08710974abe9c5ab24d282de0a9 |
| institution | Kabale University |
| issn | 2073-431X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computers |
| spelling | doaj-art-d0efb08710974abe9c5ab24d282de0a92025-01-24T13:27:52ZengMDPI AGComputers2073-431X2025-01-011411410.3390/computers14010014Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator ModelAli Hasan Ali0Muhammad Amir1Jamshaid Ul Rahman2Ali Raza3Ghassan Ezzulddin Arif4Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, IraqAbdus Salam School of Mathematical Sciences, GC University, Lahore 54600, PakistanAbdus Salam School of Mathematical Sciences, GC University, Lahore 54600, PakistanDepartment of Mathematics, Minhaj University, Lahore 54770, PakistanDepartment of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit 34001, IraqThe motivation behind this study is to simplify the complex mathematical formulations and reduce the time-consuming processes involved in traditional numerical methods for solving differential equations. This study develops a computational intelligence approach with a Morlet wavelet neural network (MWNN) to solve the nonlinear Van der Pol–Mathieu–Duffing oscillator (Vd-PM-DO), including parameter excitation and dusty plasma studies. The proposed technique utilizes artificial neural networks to model equations and optimize error functions using global search with a genetic algorithm (GA) and fast local convergence with an interior-point algorithm (IPA). We develop an MWNN-based fitness function to predict the dynamic behavior of nonlinear Vd-PM-DO differential equations. Then, we apply a novel hybrid approach combining WCA and ABC to optimize this fitness function, and determine the optimal weight and biases for MWNN. Three different variants of the Vd-PM-DO model were numerically evaluated and compared with the reference solution to demonstrate the correctness of the designed technique. Moreover, statistical analyses using twenty trials were conducted to determine the reliability and accuracy of the suggested MWNN-GA-IPA by utilizing mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and mean square error (MSE).https://www.mdpi.com/2073-431X/14/1/14Morlet wavelet neural networkgenetic algorithminterior-point algorithmstatistical analysisVan der Pol–Mathieu–Duffing oscillator modelexcitation function |
| spellingShingle | Ali Hasan Ali Muhammad Amir Jamshaid Ul Rahman Ali Raza Ghassan Ezzulddin Arif Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model Computers Morlet wavelet neural network genetic algorithm interior-point algorithm statistical analysis Van der Pol–Mathieu–Duffing oscillator model excitation function |
| title | Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model |
| title_full | Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model |
| title_fullStr | Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model |
| title_full_unstemmed | Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model |
| title_short | Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model |
| title_sort | design of morlet wavelet neural networks for solving the nonlinear van der pol mathieu duffing oscillator model |
| topic | Morlet wavelet neural network genetic algorithm interior-point algorithm statistical analysis Van der Pol–Mathieu–Duffing oscillator model excitation function |
| url | https://www.mdpi.com/2073-431X/14/1/14 |
| work_keys_str_mv | AT alihasanali designofmorletwaveletneuralnetworksforsolvingthenonlinearvanderpolmathieuduffingoscillatormodel AT muhammadamir designofmorletwaveletneuralnetworksforsolvingthenonlinearvanderpolmathieuduffingoscillatormodel AT jamshaidulrahman designofmorletwaveletneuralnetworksforsolvingthenonlinearvanderpolmathieuduffingoscillatormodel AT aliraza designofmorletwaveletneuralnetworksforsolvingthenonlinearvanderpolmathieuduffingoscillatormodel AT ghassanezzulddinarif designofmorletwaveletneuralnetworksforsolvingthenonlinearvanderpolmathieuduffingoscillatormodel |