Introduction to Scientific Computing - Tutorial 13: Recapitulation

Runge-Kutta methods
The general form of explicit Runge-Kutta method is:
where
s∑
y n+1 = y n + h b i k i
i=1
k 1 = f (t n , y n )
k 2 = f (t n + c 2 h, y n + a 21 k 1 h),
k 3 = f (t n + c 3 h, y n + (a 31 k 1 + a 32 k 2 )h),
.
k s = f (t n + c s h, y n + h(a s1 k 1 + a s2 k 2 + · · · + a s,s−1 k s−1 ))
and b i are coefficients.
1. Februar 2013 Bojana Rosic Introduction to Scientific Computing Seite 17