restart;
# IRK method by collocation
with(LinearAlgebra):
c:=Vector([1/4,1/2,3/4]);

nu:=Dimension(c);

q:=1:
for i from 1 to nu do
    q:=q*(t-c[i]);
od:
qi:=(n,tau)->unapply(q/(t-c[n]),t)(tau);

A:=Matrix(3,3):
for i from 1 to nu do
   for j from 1 to nu do
      A[j,i]:=int(qi(i,tau)/qi(i,c[i]),tau=0..c[j]); 
   od:
od:
b:=Vector(3):
for j from 1 to nu do
   b[j]:=int(qi(j,tau)/qi(j,c[j]),tau=0..1);
od:
simplify(A);

simplify(b);

for j from 0 to nu do
   ri:=int(q*t^j,t=0..1);
   if ri <> 0 then 
      break;
   fi
od;
m:=j;



#The order of this method is
m+nu;