Authors: Susmita Mall; S. Chakraverty
Addresses: Department of Mathematics, National Institute of Technology, Rourkela – 769 008, Odisha, India ' Department of Mathematics, National Institute of Technology, Rourkela – 769 008, Odisha, India
Abstract: In this paper, we have introduced a method which is based on the use of unsupervised type of regression-based algorithm (RBA) for solving ordinary differential equations (ODEs) with initial or boundary conditions. Approximate solution of differential equation is differentiable and closed analytic. Here we have used error back propagation method for minimising the error function and modification of the parameters without direct use of other optimisation techniques. Initial weights are taken as combination of random as well as by proposed regression-based method. We present the method for solving a variety of problems and the results with arbitrary and regression-based initial weights are compared. Here the number of nodes in hidden layer has been fixed according to the degree of polynomial in the regression. The present model demonstrates to get also the approximate solutions for the differential equation inside and outside of the training domain.
Keywords: ordinary differential equations; ODE; feedforward neural networks; unsupervised algorithms; back propagation; regression; neural network training.
International Journal of Mathematical Modelling and Numerical Optimisation, 2013 Vol.4 No.2, pp.136 - 149
Received: 24 Jan 2013
Accepted: 06 Mar 2013
Published online: 22 Jul 2013 *