abstract 97

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

97

Neural Networks Learning Approach to Solve Cauchy's Differential Equations (Short Communication Paper)

Vijay Kumar Kalyani, Sachin Gunjal, Prashant Malavadkar.

In this work, a novel approach based on an artificial neural network is proposed for solving Cauchy's second-order ordinary differential equations. Two examples of Cauchy's problem for second order ordinary differential equations one homogeneous linear differential equation and other nonlinear differential equation are presented to test the accuracy and efficiencies of the neural network method. A trial solution for both types of differential equations is formulated satisfying the initial conditions. The concept of the proposed neural network architecture is based on a three-layer feed-forward artificial neural network which is trained using unconstrained optimization method. Further in the present work, we have modified the MERLIN based program and used it to train the network and to optimize the connecting weights of different layers of the network. The solutions of Cauchy's differential equations obtained using the ANN model have been compared with the exact solutions as well as solutions obtained using fourth order Runge-Kutta method. The comparison depicted in the figures indicate high accuracy of this method. Moreover, the accuracy of ANN solutions subject to change in the number of nodes in the hidden layer is also studied.

Keywords: Artificial neural networks; trial function; Cauchy's differential equations; Merlin software; unconstrained optimization.

Cite this paper:

Kalyani V.K., Gunjal S., Malavadkar P.

Neural Networks Learning Approach to Solve Cauchy's Differential Equations

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 12, No.1 pp.219-237, 2024.