Design feed forward neural networks for solving ordinary intial value

The aim of this B is to design fast thesisd forward neural networks to present a method to solve initial value problem for ordinary differential equations. That is to develop an algorithm which can speedup the solution times, reduce solver failures, and increase possibility of obtaining the globally optimal solution. The applicability of this approach ranges from single ordinary differential equations, to systems of ordinary differential equations with initial condition . Also, a variant types of compute the search direction ¿k of conjugate gradient training algorithm are introduced and we describing several different training algorithms, many modified and new algorithms have been proposed for training Feed Forward Neural Network(FFNN), many of them having a very fast convergence rate for reasonable size networks. In all of these algorithms we use the gradient of the performance function( energy function) to determine how to adjust the weights such that the performance function is minimized, where the back propagation algorithm has been used to increase the speed of training. Finally, we illustrate the method by solving a variety of model problems.