VISUALIZATIONS OF PERIODIC ORBIT OF ORDINARY DIFFERENTIAL EQUATIONS

by SUN, JIAN

This thesis focuses on analyzing and implementing numerical methods to solve the periodic orbits of differential equations. It uses Microsoft MFC to create a user-friendly interface to visualize the final result. In the first part after a brief introduction we compare several integration methods, and choose the Gauss 10 as the numerical integration method for computing afterwards. In part two we introduced different approaches for finding periodic solutions of differential equations. In our case, we choose Palmore's method to compute the periodic orbits of differential equations such as Van der Pol, and the restricted three-body problem. The code is listed in the third part. The fourth part describes how to create a graphic user interface and make it user-friendlier with Microsoft MFC. The visualized periodic orbits for the restricted three-body problem are listed in final part.