Second order differential equations frequently arise in Physics and Engineering problems. The fundamental equations of electrodynamics, quantum mechanics, and even classical mechanics are cast as partial differential equations which when solved frequently lead to second order ordinary differential equations. Although it is possible to transform any
n^{ th} order ordinary differential equation to a system of
n first order equations, numerical methods have been developed to deal with second order ordinary differential equations directly.
Given a second order differential equation
y'' = f(x,y,y') methods are grouped as to whether or not
f(x,y,y') is independent of
y'.
Table of Methods for Second Order Differential Equations of the form y'' = f(x,y) 


Table of Methods for Second Order Differential Equations of the form y'' = f(x,y,y') 

