A multilayer perceptron neural network approach for the solution of hyperbolic telegraph equations

Neural networks have been extensively used for solving differential equations in the past, but they rely mostly on computationally expensive gradient-based numerical optimization procedure for solving differential equations. In this work, we are introducing a faster way to train neural networks for solving differential equations based on extreme learning machine algorithm. This algorithm is much faster as compared to traditional approaches, and it also provides highly accurate results. Reliability of the approach is tested by solving various cases of the hyperbolic telegraph equations. Solutions so obtained are compared to the results existing in the literature for analysing the accuracy of the proposed approach.