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Contents
0. Preface
0.1. Acknowledgments
1. Leapfrog
1.1. The Basic Equations
1.2. Time reversibility
1.3. A New Driver
1.4. An Extended Body Class
1.5. Minimal Changes
2. Integrators on the Menu
2.1. The Leapfrog Method
2.2. Two Different Versions
2.3. Tidying Up
2.4. A Subtle Bug
2.5. Ordering an Integrator
2.6. A Comparison test
2.7. Scaling
3. Runge Kutta
3.1. Two New Integrators
3.2. A Leapcat Method
3.3. Translating Formulas Again
3.4. Energy Conservation
3.5. Accuracy in Position
3.6. Reaching the Round-Off Barrier
4. A Fourth-Order Integrator
4.1. Coefficients
4.2. Really Fourth Order?
4.3. Comparing the Four Integrators
4.4. Fourth Order Runge-Kutta
4.5. Snap, Crackle, and Pop
4.6. An Attempt at an Analytical Proof
4.7. Shocked
5. A Complete Derivation
5.1. The One-Dimensional Case
5.2. A Change in Notation
5.3. The Auxiliary
k
Variables
5.4. The Next Position
5.5. The Next Velocity
5.6. Everything Falls into Place
5.7. Debugging All and Everything?
6. A Sixth-Order Integrator
6.1. A Multiple leapfrog
6.2. Great!
6.3. Too Good?
6.4. Spooky
6.5. An Orbit Segment
6.6. Victory
7. Yoshida's Algorithms
7.1. Recall Baker, Campbell and Hausdorff
7.2. An Eighth-Order Integrator
7.3. Seeing is Believing
7.4. The Basic Idea
7.5. Testing the Wrong Scheme
7.6. Testing the Right Scheme
8. A Two-Step Method
8.1. A Matter of Memory
8.2. Implementation
8.3. Testing
8.4. Stepping Back
8.5. Wishful Thinking.
8.6. An Old Friend
9. A Four-Step Method
9.1. Combinatorics
9.2. Checking
9.3. Implementation
9.4. Testing
9.5. A Predictor-Corrector Version
9.6. Implementation
9.7. A Logopo
9.8. Testing
10. Multi-Step Methods
10.1. An Six-Step Method
10.2. An Eight-Step Method
10.3. Very Strange
10.4. Wiggling the Wires
10.5. Testing the Six-Step Method
10.6. Testing the Eight-Step Method
11. The Hermite Algorithm
11.1. A Self-Starting Fourth-Order Scheme
11.2. A Higher-Order Leapfrog Look-Alike
11.3. A Derivation
11.4. Implementation
11.5. Testing
12. Literature References
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