The world's common rules (Quantum Physics, Electronics, Computational Chemistry and Astronomy) find their normal mathematical explanation in language of differential equations, so finding optimum numerical solution methods for these equations are very important. In this paper, using an artificial neural network (ANN) a numerical approach is designed to solve a specific system of differential equations such that the training process of the ANN calculates the optimal values for the coefficients of third order Runge Kutta method. To validate our approach, we performed some experiments by solving two body problem using coefficients obtained by ANN and also two other well-known coefficients namely Classical and Heun. The results show that the ANN approach has a better performance in compare with two other approaches.