% oliver6
b=[0,0,-0.0301628616742480082,0.210629874563219901,0.418047570946851726,0.0995092723726242877,0.278763245010808213,0.0232128987807438806];
c=[0.172263764596061938,0.344527529192123877,0.689055058384247754,0.0933588202545007754,0.511927054786087775,0.234655740106001763,0.862906203115231917,1]';
a=[0,0,0,0,0,0,0,0;
   0.344527529192123877,0,0,0,0,0,0,0;
   0,0.689055058384247754,0,0,0,0,0,0;
   0,0.174068623259567431,-0.0807098030050666558,0,0,0,0,0;
   0,0.102651392127928132,0.0964567635490965579,0.312818899109063085,0,0,0,0;
   0,-0.664793568353329342,0.0105915169557830625,0.491573724371957174,0.397284067131590868,0,0,0;
   0,0.0760572870992857777,0.0716566358290005797,-0.459125589921373665,0.230919508095684130,0.943398362012635095,0,0;
   0,-0.596314877705893211,-2.31473889865032475,5.99941153599423837,4.31365295126613521,-8.04836742194763039,1.64635671104347477,0];

% Lane-Emden
FunFcn=@(x,y) [y(2);-1-2/x*y(2)];

x0=0;h=0.1;y0=[1 0]'; 
f1=feval(FunFcn,x0+c(1)*h, y0);
f2=feval(FunFcn,x0+c(2)*h, y0+c(2)*h*f1);
f3=feval(FunFcn,x0+c(3)*h, y0+h*c(3)*f2);
f4=feval(FunFcn,x0+c(4)*h, y0+h*(a(4,2)*f2+a(4,3)*f3));
f5=feval(FunFcn,x0+c(5)*h, y0+h*(a(5,2)*f2+a(5,3)*f3+a(5,4)*f4));
f6=feval(FunFcn,x0+c(6)*h, y0+h*(a(6,2)*f2+a(6,3)*f3+a(6,4)*f4+a(6,5)*f5));
f7=feval(FunFcn,x0+c(7)*h, y0+h*(a(7,2)*f2+a(7,3)*f3+a(7,4)*f4+a(7,5)*f5+a(7,6)*f6));
f8=feval(FunFcn,x0+c(8)*h, y0+h*(a(8,2)*f2+a(8,3)*f3+a(8,4)*f4+a(8,5)*f5+a(8,6)*f6+a(8,7)*f7));
y1=y0+h*(b(1)*f1+b(2)*f2+b(3)*f3+b(4)*f4+b(5)*f5+b(6)*f6+b(7)*f7+b(8)*f8);


% error
y1(1)-(1-0.1^2/6)