Simulation Scenarios in One-Dimensional Self-Gravitating System

TL;DR

This paper evaluates various numerical solvers for simulating one-dimensional self-gravitating systems, concluding that the Leapfrog method offers the best balance of efficiency and stability for such simulations.

Contribution

It compares multiple numerical methods for solving gravitational systems and demonstrates the effectiveness of the Leapfrog method in this context.

Findings

Leapfrog method outperforms others in energy conservation and stability

Finite difference and Fourier methods effectively solve Poisson's equation

Simulation shows realistic phase-space evolution of the system

Abstract

We study and compare different numerical differential equation solvers on the basis of numerical complexity, energy conservation, and stable solution in phase-space for the Simple Harmonic Oscillation (SHM) problem. We conclude and show that the Leapfrog method is the best for our problem. We solve Poisson's equation in gravity on the computation grid by the finite difference method and Fourier method. We solve Poisson's equation for source not in a grid point by cloud-in cell method. Finally, we simulate one-dimensional self-gravitating system and show the evolution of the system via phase-space trajectories.