Transcendental equation solver: A novel neural network for solving transcendental equation

In this paper, we propose a novel method called transcendental equation solver (TES) for solving transcendental equations. The TES comprises a generator defined by a neural network and a discriminator defined by the mathematical expression of the transcendental equation. First, a large amount of random noise is input into the TES generator to generate the solutions of the equation; subsequently, the solution is input into the discriminator and the discriminator calculates the error between the discriminator output and the true value. Moreover, this error can update the parameters in the generator with the backpropagation algorithm. The experimental results proved that the TES exhibits an improvement in accuracy, convergence speed, and stability compared to the other methods for solving transcendental equations. © 2022 Elsevier B.V.