Approximate Analytic Solution of Burger Huxley Equation Using Feed-Forward Artificial Neural Network

Abstract

Solutions of non-linear partial differential equations of Burgers Huxley type are obtained using a feed-forward artificial neural network technique. Solution process requires minimization of an error function which is constructed by making use of the differential equation and the associated initial and boundary conditions. The minimization is carried out using the Quasi Newton algorithm employed through Matlab optimization toolbox. The solutions that are obtained using the technique are analytic in nature and have excellent generalization properties. Results are compared with the existing solutions to validate the utility and effectiveness of proposed procedure. Effect of variation in number of training points on solution accuracy is also studied through calculation of numerical rate of convergence. Solutions obtained using the neural network technique are analytic in nature and can be obtained directly without linearising non-linear partial differential equations.