2-Step Runge Kutta - Example

The 2-step RK method is pretty much the same as the Euler’s method performed with two time steps. The 2-step RK method was used to solve the problem E2 from W.H. Enright & J.D. Pryce (Two Fortran packages for assessing initial value methods, ACM Trans. On Mathematical Software, Vol. 13, No. 1, 1987, pp 1-27). This is the series of equations defined by

 

 

 with y1(0)=2, y2(0)=0. The result is shown below for a step size 0.005.