Research Information System
5TH INTERNATIONAL ARTIFICIAL INTELLIGENCE AND DATA SCIENCE CONGRESS (ICADA 2025) , Zonguldak, Turkey, 24 - 25 April 2025, pp.514-522, (Full Text)
This study presented a new method for solving the pantograph type differential equations with various initial and boundary conditions using the Jacobi Neural Network (JNN). Jacobi polynomials are used as activation functions in the middle layer of the neural network, so the architecture has been called Jacobi neural network. The trial solution of the pantograph type differential equation is considered as the output of the feed-forward neural network. The neural network consists of adjustable weights with Newtons’ like method. The architecture of the JNN consists of three layers named input layer, hidden layer and output layer. In the input layer, an independent variable is given. In the hidden layer, Jacobi polynomials have been used to activate the input from the input layers. The output layer consists of a linear combination of the inputs with weights of the hidden layer. Various problems have been solved by the presented method for the effectiveness of the method. The JNN solutions are compared with different methods. In the application of the method, the convergence of the weights and its stability were examined.