5a. A Better Integrator

• Recap of integration schemes
• Reminder: the predictor-corrector scheme

• Comparison of second-order schemes
  • simple versus analytic 2nd order
  • simple versus numerical 2nd order
  • analytic versus numerical 2nd order

• Scaling comparison of the three schemes.

• In-class exercise 5.1: Long-term behavior of the second-order integration schemes

• Demonstration: comparison of orders and accuracy of various schemes

• Properties of the improved scheme
  • second-order accuracy
  • time-reversibility and conservation laws
  • long-term stability