Solving transcendental equation using artificial neural network

Abstract

Transcendental equations play important role in solving various science and engineering problems. There exist many transcendental equations, which may not be solved by usual numerical methods. Accordingly, this paper gives a novel idea for solving transcendental equations using the concept of Artificial Neural Network (ANN). Multilayer Network architecture (viz. Four-layer network architecture) has been proposed for solving the transcendental equation. The detail network architecture with the procedures to solve single and system of transcendental equations have been discussed. The weights from input layer to the first hidden layer consist of the unknown variable and other weights in different layers are the known coefficients with respect to the given transcendental equation. After training by proposed steps and back propagation technique starting with a guess value(s), the unknown variable(s) tend to converge depending upon the accuracy thereby giving the solution of the equation. Few standard example problems have been presented to validate the proposed method. Further, two examples have been included to show the applicability of the ANN method in comparison to the well-known numerical method. Moreover, an application problem of junction diode circuit has also been addressed.