1. Introduction 2. Harmonic Balance Method and Time Domain Collocation Method 3. Dealiasing for Harmonic Balance and Time Domain Collocation Methods 4. Application of Time Domain Collocation in Formation Flying of Satellites 5. Local Variational Iteration Method 6. Collocation of Local Variational Iteration Method 7. Application of Local Variational Iteration Method in Orbital Mechanics 8. Applications of Local Variational Iteration Method in Structural Dynamics