restart;

digit := 15;

F[0] := fw;

F[1] := delta*F[2]+epsilon;

F[2] := A;

T[0] := B;

T[1] := -1;

a := 0.01;

m := 1;

M := 1;

lambda := 1;

b := 1;

fw := 1;

epsilon := 1;

delta := 1;

Pr := 6;

Ec := 1;

R := 1;

for k from 0 to 7 do F[k+3] := (a*(sum((i+1)*(i+2)*F[i+2]*(k-i+1)*T[k-i+1], i = 0 .. k))-m(1+a*T[k]-(sum((i+1)*F[i+1]*(k-i+1)*F[k-i+1], i = 0 .. k))+a*(sum(sum(T[i]*(r-i+1)*F[r-i+1]*(k-r+1)*F[k-r+1], i = 0 .. r), r = 0 .. k)))-M*(1-(k+1)*F[k+1]+a*T[k]-a*(sum(T[i]*(k-i+1)*F[k-i+1], i = 0 .. k)))-((m+1)*(1/2))*(sum((i+1)*(i+2)*F[i+2]*F[k-i], i = 0 .. k)+a*(sum(sum(T[i]*F[k-r]*(r-i+1)*(r-i+2)*F[r-i+2], i = 0 .. r), r = 0 .. k)))-lambda*(T[k]+a*(sum(T[i]*T[k-i], i = 0 .. k))))/((k+1)*(k+2)*(k+3)); T[k+2] := (-(1+b/Pr)*(k+1)*T[k+1]-b*(sum(T[i]*(k-i+1)*T[k-i+1], i = 0 .. k))-M*Ec*(1-(2*(k+1))*(k+2)*F[k+2])-Ec*(1+M)*(sum((i+1)*(i+2)*F[i+2]*(k-i+1)*(k-i+2)*F[k-i+2], i = 0 .. k))-(1-2*m)*(sum(T[i]*(k-i+1)*F[k-i+1], i = 0 .. k))-((m+1)*(1/2))*(sum(F[i]*(k-i+1)*T[k-i+1], i = 0 .. k)))/((4/3)*R*(k+1)*(k+2)) end do;

FF := sum(F[j]*y^j, j = 0 .. 5);

TT := sum(T[j]*y^j, j = 0 .. 5);

with(numapprox); pade(FF, y, [4, 4]);

pade(diff(FF, y), y, [4, 4]);

pade(TT, y, [4, 4]);

solve({limit(pade(TT, y, [4, 4]), y = infinity) = 0, limit(pade(diff(FF, y), y, [4, 4]), y = infinity) = 1}, [A, B]);