Runge-Kutta Method for Solving

Two Coupled 1st Order Differential Equations

or One 2nd Order Differential Equation

The solutions to the two coupled 1st order differential equations:

can be obtained by the Runge-Kutta method, correct to fourth order terms in x, using

The incremental results are:

These equations can easily be extended to systems of N differential equations. They can also be used in solving 2nd order differential equations if the functions F and G are taken as follows: