A Brief Survey of Issues Relating to the Reliability of Simulation of the Large Gravitational N-body Problem

Wayne Hayes

Ph.D. Qualifying Depth paper, Computer Science Department, University of Toronto

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Start: Introduction

Note to readers: Those unfamiliar with common terms from stellar dynamics like softening, collision, regularization, etc., should probably read the glossary first.

Table of Contents

• Introduction
• N-body simulation
  • Softening and discreteness noise
  • Statistics of collisional N-body simulations
    • Efficiency of many small vs.  one large simulation
  • Exponential divergence in N-body systems
• Integrators
• Miscellaneous comments concerning dynamical systems
• Shadowing
  • Introduction
  • Tutorial
  • Shadowing non-hyperbolic systems
  • Refinement of a numerical trajectory
    • QT's generalization to arbitrary Hamiltonian systems
    • Discussion and Results of the GHYS/QT algorithm
  • Shadowing Lemmas, and theoretical results
    • Shadowing lemmas for discrete maps
    • Shadowing lemmas for ODE systems
• Two-point Boundary Value Problems for ODEs
• Discussion and future directions
• Glossary
• References
• About this document ...

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