Abstract: Two numerical methods for solving time varying periodic coefficient Lyapunov differential equations are proposed, both of which are based on Fourier series expanding and the precise integration method. The first algorithm is a dimension expanding method, and the second one solves the Lyapunov equations by using the solutions for homogeneous Riccati equations. The methods in this paper have been proved correct and reliable by numerical examples. Numerical results also show that the homogeneous Riccati equation method is better than the dimension expanding method on accuracy and efficiency, while dimension expanding method is more suitable for Lyapunov equations that cannot be solved by the homogeneous Riccati equation method.