Cascade-Forward Neural Network for Volterra Integral Equation Solution

Abstract

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural network is trained multi times to obtain the desired output, the training of cascade-forward neural network model terminal when there is no enhancement in result. The model combines all training cascade-forward neural network to obtain the best result. This method proved its successful in training and testing cascade-forward neural network for obtaining the desired output of numerical solution of volterra integral equation for multi intervals. Cascade-forward neural network model measured by calculating MSE to compute the degree of error at each training time.