Abstract
In this paper, a deep learning algorithm based on Deep Galerkin method (DGM) is presented for the approximate solution of the generalized Burgers–Huxley equation (gBHE), and generalized Huxley’s equation (gHE). In this method, a deep neural network (DNN) is used for approximating the solution without generating mesh grid, which satisfies the differential operator, boundary and initial conditions. DNN is trained on randomly selected batches of time and space points, thus helping to avoid forming a mesh. Adam optimizer is used for optimizing the parameters of the DNN. Further, the convergence of the cost function and convergence of the neural network to the exact solution is demonstrated. This method shows very encouraging results which have been compared with recent methods such as: A fourth order improved numerical scheme (FDS4), Adomain-decomposition method (ADM), Modified cubic B-spline differential quadrature method (MCB-DQM), Variational iteration method (VIM), and others.
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