Wavelet Neural Network Solutions for Riccati Differential Equations: The Vieta-Fibonacci Approach

To propose the computational method for obtaining the numerical solutions for Riccati differential equations is the primary focus of this work. Riccati differential equations are important because they are applicable to a wide range of physical and engineering phenomena. Riccati differential equations are still extremely difficult to solve using conventional or contemporary numerical methods due to their inherent nonlinearity. By applying the basic ideas of Vieta-Fibonacci wavelets, this study presents an artificial neural network based method for effectively solving the nonlinear Riccati differential equations. In addition, the problem is solved using a single-layer functional link neural network. The proposed numerical method is applied to solve various cases of Riccati differential models. The obtained numerical results indicate a higher level of congruence between the approximate and exact values, proving the accuracy and efficiency of the proposed method.