@tomleslie i love your coding style and pattern. i really got this problems from the following JOURNALS

1. Hydromagnetic Flow and Heat Transfer Past a Continuously Moving Porous Boundary.(P. Chandran, N.C     Sacheti and A.K Singh) 1996

2. Effect of Transverse Magnetic field on a flat plate thermometer.(A.K Singh, P.Chandran, N.C. Sacheti) 1998

I observed that f(eta=0) values are CORRECT but theta(eta=0) values are WRONG in both journals.

Please, i will be glad if you can HELP me check the Journal2 also.

>restart;
with (plots):ode1:=diff(f(eta),eta,eta,eta)+1/2*f(eta)*diff(f(eta),eta,eta)+M*(1-diff(f(eta),eta))=0:

>ode2:=diff(theta(eta),eta,eta)+1/2*Pr*f(eta)*diff(theta(eta),eta)=-2*Pr((diff(f(eta),eta,eta))^2+M*(diff(f(eta),eta))^2):

>bcs1:= f(0)=0, D(f)(0)=0,D(f)(10)=1:

fixedparameter:=[Pr=0.71]:
>ode3:=eval(ode2,fixedparameter):

>bcs2:= theta(10)=0,D(theta)(0)=0:
L:=[0.00,0.02,0.04,0.06]:

>for k from 1 to 4 do
sol_All:=dsolve(eval({ode1,ode3,bcs1,bcs2},M=L[k]),[f(eta),theta(eta)],numeric,output=listprocedure):
Y_sol||k:= rhs(sol_All[4]);
YP_sol||k:=rhs(sol_All[5]);
end do:
>for k from 1 to 4 do
evalf[3](L[k]),evalf[7]((Y_sol||k(0))),evalf[7](YP_sol||k(0));       
od;
                    0., 0.3320573, 15.02141
                   0.02, 0.3588413, 14.79601
                   0.04, 0.3839690, 14.60015
                   0.06, 0.4077149, 14.42746

THE CORRECT ANSWER IS GIVEN AS ----FROM THE JOURNAL2
                   0.,     0.33206, 0.84188
                   0.02, 0.35884, 1.14112
                   0.04, 0.38397, 1.44022
                   0.06, 0.40771, 1.73206