الملخص

  In this research, we use artificial neural networks, specifically radial basis function neural network (RBFNN) to improve the performance and work of the explicit finite differences method (EFDM), where it was compared, the modified method with an explicit finite differences method through solving the Murray equation and showing by comparing results with the exact solution that the improved method by using  (RBFNN) is the best and most accurate by giving less error rate through root mean square error (RMSE) from the classical method (EFDM).