Dear @vanta5,

i suggest the mention boundry condtions are not well posed, because f'(0)=1

and u should adjust the code in this formet 

b := 1;
ode1 := diff(f(x), x, x, x)+3*f(x)*(diff(f(x), x, x))-2*(diff(f(x), x))^2+g(x) = 0;
ode2 := diff(g(x), x, x)+(3*10)*f(x)*(diff(g(x), x)) = 0;
bcs1 := (D(f))(0) = 1, f(0) = 0, (D(f))(b) = 0;
bcs2 := g(0) = 1, g(b) = 0;
sys := {bcs1, bcs2, ode1, ode2};
dsn := dsolve(sys, numeric);
print(plots:-odeplot(dsn, [x, diff(f(x), x)], 0 .. b, color = black))
print(plots:-odeplot(dsn, [x, g(x)], 0 .. b, color = black))

@sipeiw
 plz follow Mr. rlopez, he guess it in right direction...

@Preben Alsholm its great job, but if you got better then this kindly inform me. because i have same field of intrest but not enough good in coding, 

thanks
r.haq.qau@gmail.com 

hi,
   how you can plot f''(0) and theta'(0) against Pr.
 thanks

restart:ShootLib := "C:/MP/Shoot9/":
> libname := ShootLib, libname:
> with( Shoot ):
> with(plots):with(LinearAlgebra):
> A:=0:
> FNS:={ f(z), G(z), H(z)}:
> ODE:={diff(f(z),z)  = G(z),
>       diff(G(z),z)  = H(z),
>       diff(H(z),z)  = -f(z)*H(z)-G(z)*(1-G(z))-A*(G(z)-1+0.5*z*H(z))}:
> IC:={f(0)=s, G(0)=1+lambda1,H(0)=1}:
> BC:={G(9)=1}:
> infolevel[shoot]:=1:
> S:=shoot( ODE, IC, BC, FNS,[lambda1=0,s=1] ):

you can adjust this command w.r.t your own problem???

d1 := subs(epsilon = 0.5e-1, s = 0.5e-1, gamma = 0.5e-1, Nr = .3, Nb = .2, Nt = .1, M = .5,
               Le = 1, [de1]);

da1 := seq( dsolve( subs(Pr=.1*i, d1), numeric, output = procedurelist), i=1..10):

I make a plot for θ'(0) against Pr:

points := seq( [.1*i, subs(da1[i](0), diff(theta(eta), eta))], i=1..10 );

plot([points]);

if u did it then must reply, and whats your own email id? 

ok, let the above mention problem is in more easy form.... How we can solve it for dual solutions and graphs now????


f'''(x)+f(x)f''(x)+[f'(x)]^2-A*{f'(x)-(x/2)*f''(x)}=0,

g''(x)+P*[f(x)*g'(x)]=0,

Boundary conditions

f(0)=k, f '(0) =-1,f '(infinity)=1,
g(0)=1,  g(infinity)=0.

 thanks

how we can calculate the doual solution??????  

Dear J4James,
its not working in maple 15 and 16.

Still stuck for may 1st mention problem....... :-( 

restart:
ShootLib := "C:/khan/Shoot9/":
libname := ShootLib, libname:
with( Shoot ):
Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received Shoot
with(plots):with(LinearAlgebra):
A:=0.01:pr:=0.7:
FNS:={ f(z), g(z), G(z), H(z), M(z) }:
ODE:={diff(f(z),z)  = G(z),
      diff(G(z),z)  = H(z),
      diff(H(z),z)  = -f(z)*H(z)-1+G(z)^2-A+A*G(z)+A*0.5*z*H(z),
      diff(g(z),z) = M(z),                                                                                                                                                                                                            diff(M(z),z) = -pr*f(z)*M(z)+pr*g(z)*G(z)+pr*A*g(z)+pr*A*0.5*z*G(z)}:
IC:={g(0)=1, f(0)=f0, G(0)=epsilon, M(0)=0, H(0)=1}:
BC:={g(8)=0, G(8)=1}:
infolevel[shoot]:=1:
S:=shoot( ODE, IC, BC, FNS,[f0=-0.1, epsilon=-1.18] ):

odeplot(S,[ [z,g(z)] ], 0..8);

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
odeplot(S,[ [z,G(z)] ], 0..8);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

Good effort but graphical results not match with this article that i mention above

Unsteady stagnation point flow and heat transfer over a stretching/shrinking sheet with suction or injection 
by M. Suali, N.M.A Nik long 

what do you think if you have shoot command example ??? and what i suggust above two sites.

thanks 

Thanks for help. This command is very use full for my problem.

Respectd Sir, 
 you did great job but i still still stuck over here.

Actual problem is. 

#given system of equations are,

1. diff(alpha*f(y),y,y,y,y)+G*(diff(theta(y),y,y))+ B*(diff(phi(y),y,y))+6* beta*(diff(f(y),y,y))*(diff(f(y),y,y,y))^(2)+3* beta*(diff(f(y),y,y,y,y))*(diff(f(y),y,y))^(2)=0  
2. diff(theta(y),y,y)+Nb*diff(theta(y),y)*diff(phi(y),y)+Nt*(diff(theta(y),y))^(2)=0,  
3. diff(phi(y),y,y)+Nb/(Nt)*diff(theta(y),y,y)=0, 

#boundary conditions,
     4.  f(y) = (1/2)*F, (D(f))(y)=-1,  theta(y) = 0,  phi(y) = 0   at    y=h1=1+a*cos(x)

     5.  f(y) = -(1/2)*F, (D(f))(y)=-1,  theta(y) = 1, phi(y) = 1   at    y=h2= -d-b*cos(x+omega)

#Rate of Pressure with respect to x is define as. 

     6.  (dp/dx)=alpha+3*beta*(diff(f(y), y, y))^2)*(diff(f(y), y, y, y))+G*theta(y)+B*phi(y)

#Notice that: after calculating numerically equations 1-5, keeping fix values of parameters mention in last question, then substituting the values diff(f(y), y, y), diff(f(y), y,,y y), theta(y) and phi(y) into Equation (6) that u did in your last answer. but  (dp/dx) should remain the funation of x.

     7.  Δp=Int( (dp/dx),0..1)
#Q is wave frame define as,
     8.  Q=F+1+d 
# Plot ΔP againt Q(-3..3) 

k*(f(eta)^2*(diff(f(eta), eta))

is replace to get solution 

k*(f(eta)^2*(diff(f(eta), eta,eta,eta))