EulerError:=Series[t f[x],{t,0,4}]-Integrate[Series[f[x+t],{t,0,4}],t]


HeunError:=Series[x[0]+ (t/2)*( f[x[0]] + f[x[0]+f[x[0]] t]), {t,0,3}] -
                Series[x[t],{t,0,3}]
                
k1=f[x[0]] t;
k2=f[x[0]+k1/2] t;
k3=f[x[0]+k2/2] t;
k4=f[x[0]+k3] t;
  

RungeError:=Simplify[Series[x[0]+(k1 +2 k2+ 2 k3 +k4)/6,{t,0,4  }] -
              Series[x[t],{t,0,4}]]
