Design of Morlet Wavelet Neural Networks for Solving the Nonlinear Van der Pol–Mathieu–Duffing Oscillator Model - Ali Hasan Ali; Muhammad Amir; Jamshaid Ul Rahman; Ali Raza; Ghassan Ezzulddin Arif (Computers)
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).