Numerical Solution of Differential Equations by the Parker-Sochacki Method

TL;DR

This paper provides a tutorial on the Parker-Sochacki method for numerically solving differential equations, illustrating its application through projectile motion and the N-body gravitational problem.

Contribution

It introduces and explains the Parker-Sochacki method, a numerical technique for solving systems of differential equations, with practical examples.

Findings

Effective numerical solutions for projectile motion.

Successful application to the Newtonian N-body problem.

Demonstrates the method's versatility and accuracy.

Abstract

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.