Module 4: Systems of Equations and Equations of Order Greater Than One
  Lecture 13: Direct Methods For Higher Order Equations
 

 

Runge-Kutta Methods:

Let us consider the second order equation

.

we know . A general two-stage explicit Runge-Kutta method has the form

(4.6)

Expanding we get

(4.7)

where everything is evaluated at . We also have