+ + + ...

The second-order Runge-Kutta method IS obtained by assuming that L1y = (Yn+' - Yn) is a weighted sum of two L1y's:

where L1y, is given by the explicit Euler FDE:

and L1Y2 is based onj(t,y) evaluated somewhere in the interval tn < t < tn+l :

(7.158)

(7.159)

(7.160) where a and (3 are to be determined. Let L1t = h. Substituting L1y, and L1Y2 into Eq. (7.158) gives

Expressing jet, y) in a Taylor series at grid point n gives - - -j(t,y) = In +ftln h +/yIn L1y + ...