Contents

• 0. Preface
• 0.1. xxx
• 1. First-Order Differential Equations
• 1.1. Starting at Square One
• 1.2. Keeping it Simple
• 1.3. Notation
• 1.4. A Matter of Interpretation
• 1.5. Taylor Series
• 1.6. New Force Evaluations
• 1.7. One Force Evaluation per Step
• 1.8. Two Force Evaluations per Step
• 1.9. A One-Parameter Family of Algorithms
• 2. Recycling Force Evaluations
• 2.1. One Force Evaluation per Step
• 2.2. What is Good Enough?
• 2.3. Approximate Recycling
• 2.4. Summary
• 2.5. Two Force Evaluations per Step
• 2.6. Two Examples
• 2.7. Recycle Conditions
• 2.8. Remaining Freedom
• 2.9. Summary
• 3. Second-Order Differential Equations
• 3.1. Formulating the Problem
• 3.2. Vector Notation
• 3.3. One Force Evaluation per Step
• 3.4. Not So Fast
• 3.5. Forward Euler in Vector Form
• 3.6. Two Force Evaluations per Step
• 3.7. Putting Everything Together
• 3.8. Summary
• 3.9. Two Examples
• 4. Partitioned Runge-Kutta Algorithms
• 4.1. One Force Evaluation per Step
• 4.2. xxx
• 4.3. Two Force Evaluations per Step
• 5. Recycling Force Evaluations
• 5.1. One Force Evaluation per Step
• 5.2. Two Force Evaluations per Step
• 6. Literature References