The various methods are published for satellite orbit propagation and the numerical integration is one of the most common methods. The numerical integrators can be divided into two main methods, Single-Step and Multi-Step methods. In this paper, the results of Runge-Kutta method as the most common Single-Step method and prediction-estimation-correction-estimation method as the most common Multi-step method are compared. In this paper, it is proved that if the error-controlled integration methods are used, the difference between Single-step and Multi-step methods would be at sub-millimeter level. In this paper, the Lagrange method is introduced as a semi-analytical method too and the Lagrange coefficients are developed from central field to full gravitational field of Earth. By this development, the Lagrange method can be used in LEO satellite orbit determination. The results show that the accuracy of the Lagrange method for LEO satellite orbit determination is about 5 millimeter over one day.