# Runge Kutta method for s=2 and order p=2 
s:=2: p:=2:
D(y):=t->f(t,y(t)):
# Taylor series of solution
TaylorPhi:=convert(taylor(y(t+dt),dt=0,p+1),polynom);
TaylorPhi:=normal((TaylorPhi-y(t))/dt);
# Taylor series of RK-method
k[1]:=f(t,y(t));
k[2]:=taylor(f(t+c[2]*dt,y(t)+a[2,1]*k[1]*dt),dt=0,p);
RungeKuttaPhi:=b[1]*k[1]+b[2]*k[2];
RungeKuttaPhi:=convert(RungeKuttaPhi, polynom);
d:=expand(TaylorPhi-RungeKuttaPhi);
vars:={c[2],b[1],b[2],a[2,1]};
eqns:={coeffs(d,indets(d) minus vars)};
solve(eqns,vars);