I am trying to get the output of the system of ODE in the mesh form. Can I set the step length for range? when I use range=0..10 it takes many values whereas I only need the values for integers between 0 and 10 inclusive.

Dear All,

How do I use the piecewise function z[k]:=piecewise(k<>0,0,k=0,1) in the loop 

for k from 0 to 10 do

(sum((m^2-1)/z(z[k]+1),m,0..k))

end:

i want the value of z[k] to be automatically used in the loop for the corresponding value of k

How do I extract the real solutions of a polynomial that has solutions both in real and complex domains?

restart;
Digits:=4:
n:=11:
M := 2:
Le := 5:
Lb := 2:
L:= 1:
l := 0.5:
Pr := 1:
Pe := 2:
Nt := 0.5:
Nb := 0.8:
F[0]:=0:
F[1]:=l*F[2]:
F[2]:=a:
T[0]:=1:
T[1]:=b:
d:=k->piecewise(k<>0,0,k=0,1):
for k from 0 to n do F[k+3]:=-1/(d(k)+(k+1)*(k+2)*F(k+2))*((sum(F[k-m]*(m+1)*(m+2)*F[m+2],m=0..k))-(sum((k-m+1)*(m+1)*F[k-m+1]*F[m+1],m=0..k))-M*(k+1)*F[k+1])*(factorial(k)/factorial(k+3));
T[k+2]:=-1*(Pr/(k+1)*(k+2))*((sum(F[k-m]*(m+1)*T[m+1],m=0..k))+Nt*(sum((k-m+1)*(m+1)*T[k-m+1]*T[m+1],m=0..k))+Nb*(sum((k-m+1)*(m+1)*T[k+1]*F[k-m+1],m=0..k))) end do: 
f:=sum(F[k]*y^k,k=0..n); 
t:=sum(T[k]*y^k,k=0..n); 
with(numapprox):
pade(diff(f,y),y,[4,4]):
pade(t,y,[4,4]):
solve({limit(pade(diff(f,y),y,[4,4]),y=infinity)=0.,limit(pade(t,y,[4,4]),y=infinity)=0.,[a,b]);