Contents

• Preface
• Acknowledgments
• Leapfrog
• The Basic Equations
• Time reversibility
• A New Driver
• An Extended Body Class
• Minimal Changes
• Integrators on the Menu
• The Leapfrog Method
• Two Different Versions
• Tidying Up
• A Subtle Bug
• Ordering an Integrator
• A Comparison test
• Scaling
• Runge Kutta
• Two New Integrators
• A Leapcat Method
• Translating Formulas Again
• Energy Conservation
• Accuracy in Position
• Reaching the Round-Off Barrier
• A Fourth-Order Integrator
• Coefficients
• Really Fourth Order?
• Comparing the Four Integrators
• Fourth Order Runge-Kutta
• Snap, Crackle, and Pop
• An Attempt at an Analytical Proof
• Shocked
• Orbit vs. Interaction
• Space and Time Dependent Interactions
• The One-Dimensional Case
• A Change in Notation
• The Auxiliary _k_ Variables
• The Next Position
• The Next Velocity
• Everything Falls into Place
• Debugging All and Everything?
• A Sixth-Order Integrator
• A Multiple leapfrog
• Great!
• Too Good?
• Spooky
• An Orbit Segment
• Victory
• Yoshida's Algorithms
• Recall Baker, Campbell and Hausdorff
• An Eighth-Order Integrator
• Seeing is Believing
• The Basic Idea
• Testing the Wrong Scheme
• Testing the Right Scheme
• A Two-Step Method
• A Matter of Memory
• Implementation
• Testing
• Stepping Back
• Wishful Thinking.
• An Old Friend
• A Four-Step Method
• Combinatorics
• Checking
• Implementation
• Testing
• A Predictor-Corrector Version
• Implementation
• A Logopo
• Testing
• Multi-Step Methods
• An Six-Step Method
• An Eight-Step Method
• Very Strange
• Wiggling the Wires
• Testing the Six-Step Method
• Testing the Eight-Step Method
• The Hermite Algorithm
• A Self-Starting Fourth-Order Scheme
• A Higher-Order Leapfrog Look-Alike
• A Derivation
• Implementation
• Testing
• Literature References