An Effective and Efficient Method to Solve the High-Order and the Non-Linear Ordinary Differential Equations: the Ratio Net

An effective and efficient method that solves the high-order and the non-linear ordinary differential equations is provided. The method is based on the ratio net. By comparing the method with existing methods such as the polynomial based method and the multilayer perceptron network based method, we show that the ratio net gives good results and has higher efficiency.