Ahmad Shirzadi

In this thesis, we propose an algorithm for solving differential equations using the Bernstein neural network model. In the proposed method, a single-layer Bernstein neural network with functionally connected components is introduced. The proposed learning algorithm is based on the use of the mean squared error index and employs the steepest descent algorithm. Numerical results for second-order ordinary differential equations, systems of ordinary differential equations, second-order elliptic partial differential equations, and fourth-order equations with various boundary conditions are reported, demonstrating the effectiveness of the proposed approach. All computations were performed using MATLAB software.