function [a,b,c,est]=rkf78
c = [0 2/27 1/9 1/6 5/12 1/2 5/6 1/6 2/3 1/3 1 0 1]';
a =[zeros(1,13);2/27 zeros(1,12);1/36 1/12 zeros(1,11);
   1/24 0 1/8 zeros(1,10);5/12 0 -25/16 25/16 zeros(1,9);
   1/20 0 0 1/4 1/5 zeros(1,8);-25/108 0 0 125/108 -65/27 125/54 zeros(1,7);
   31/300 0 0 0 61/225 -2/9 13/900 zeros(1,6);
   2 0 0 -53/6 704/45 -107/9 67/90 3 zeros(1,5);
   -91/108 0 0 23/108 -976/135 311/54 -19/60 17/6 -1/12 zeros(1,4);
   2383/4100 0 0 -341/164 4496/1025 -301/82 2133/4100 45/82 45/164 18/41 0 0 0;
   3/205 0 0 0 0 -6/41 -3/205 -3/41 3/41 6/41 0 0 0;
   -1777/4100 0 0 -341/164 4496/1025 -289/82 2193/4100 51/82 33/164 12/41 0 1 0];
s=41/840;
b =[zeros(1,5) 34/105 9/35 9/35 9/280 9/280 0 s s]';
est=[s zeros(1,9) s -s -s]';