Numerical Solutions of Ordinary Differential Equations

Abstract

This paper explains the methods of Runge-Kutta, Adams-Bashforth and Bullruch-Stoer for approximating the solution of a first order initial value problem, and the Numerov method for appromating the solution for a class of second-order linear initial value problems. Mathematica is used to derive some of the formulas, solve the example equations, and plot the solutions.