Hi

Im going to solve mixing layer boundary layer equation in maple but Its this error: "Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point"

please help me. thank you.

> restart;
> alias(U = u(x, y), V = v(x, y)); PDE := {diff(U, x)+diff(V, y) = 0, U*(diff(U, x))+V*(diff(U, y))-nu*(diff(U, `$`(y, 2))) = 0};
print(`output redirected...`); # input placeholder
    // d   \   / d   \        / d   \     / d   \      / d  / d   \\    \ 
   { |--- U| + |--- V| = 0, U |--- U| + V |--- U| - nu |--- |--- U|| = 0 }
    \\ dx  /   \ dy  /        \ dx  /     \ dy  /      \ dy \ dy  //    / 
> simsubs := eta(x, y) = y*sqrt((1/2)*u[0]/(nu*x));
print(`output redirected...`); # input placeholder
                                                  (1/2)
                                 1    (1/2) /u[0]\     
                     eta(x, y) = - y 2      |----|     
                                 2          \nu x/     
> stream := psi(x, y) = sqrt(2*nu*x*u[0])*f(eta(x, y));
print(`output redirected...`); # input placeholder
                           (1/2)            (1/2)             
              psi(x, y) = 2      (nu x u[0])      f(eta(x, y))
> Usubs := U = diff(rhs(stream), y);
print(`output redirected...`); # input placeholder
              (1/2)            (1/2)                 / d           \
         U = 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
                                                     \ dy          /
> Vsubs := V = -(diff(rhs(stream), x));
print(`output redirected...`); # input placeholder
               (1/2)                     
              2      f(eta(x, y)) nu u[0]
        V = - ---------------------------
                               (1/2)     
                  2 (nu x u[0])          

              (1/2)            (1/2)                 / d           \
           - 2      (nu x u[0])      D(f)(eta(x, y)) |--- eta(x, y)|
                                                     \ dx          /
> ODE := simplify(subs(Usubs, Vsubs, simsubs, PDE));
print(`output redirected...`); # input placeholder
 /                             /      /           /                 (1/2)\  /    
 |                  1          |    2 |           |1    (1/2) /u[0]\     |  |1   
 |0 = 0, - ------------------- |u[0]  |@@(D, 2)(f)|- y 2      |----|     | f|- y 
<                        (1/2) \      \           \2          \nu x/     /  \2   
 |               2 /u[0]\                                                        
 |         2 nu x  |----|                                                        
 \                 \nu x/                                                        

               (1/2)\          (1/2)  
   (1/2) /u[0]\     |    /u[0]\       
  2      |----|     | nu |----|      x
         \nu x/     /    \nu x/       

                                 /                 (1/2)\\\    \ 
                (1/2)            |1    (1/2) /u[0]\     |||    | 
   + (nu x u[0])      @@(D, 3)(f)|- y 2      |----|     ||| = 0| 
                                 \2          \nu x/     ///     >
                                                               | 
                                                               | 
                                                               / 
> simsubs2 := solve(subs(eta(x, y) = eta, simsubs), {y});
print(`output redirected...`); # input placeholder
                              /         (1/2) \ 
                              |    eta 2      | 
                              |y = -----------| 
                             <           (1/2) >
                              |    /u[0]\     | 
                              |    |----|     | 
                              \    \nu x/     / 
> ODE := simplify(subs(simsubs2, ODE), symbolic);
print(`output redirected...`); # input placeholder
      /             2                                                 \ 
      |         u[0]  (@@(D, 2)(f)(eta) f(eta) + @@(D, 3)(f)(eta))    | 
     < 0 = 0, - -------------------------------------------------- = 0 >
      |                                2 x                            | 
      \                                                               / 
> 
> shootlib := "C:\\Users/abbas/Desktop/maple9/"; libname := shootlib, libname; with(Shoot);
print(`output redirected...`); # input placeholder
                                   [shoot]
> FNS := {f(eta), g(eta), h(eta)};
> ODE := {diff(f(eta), eta) = g(eta), diff(g(eta), eta) = h(eta), diff(h(eta), eta) = -f(eta)*h(eta)};
print(`output redirected...`); # input placeholder
 /  d                      d                      d                          \ 
{ ----- f(eta) = g(eta), ----- g(eta) = h(eta), ----- h(eta) = -f(eta) h(eta) }
 \ deta                   deta                   deta                        / 
> IC := {f(0) = 0, g(0) = 0, h(0) = beta};
print(`output redirected...`); # input placeholder
                      {f(0) = 0, g(0) = 0, h(0) = beta}
> BC := {g(-10.) = 0, g(10.) = 1, limit(eta-f(eta), eta = 10) = 0};
print(`output redirected...`); # input placeholder
                  {10 - f(10) = 0, g(-10.) = 0, g(10.) = 1}
> infolevel[shoot] := 1;
print(`output redirected...`); # input placeholder
                                      1
> S := shoot(ODE, IC, BC, FNS, beta = 0, abserr = 0.5e-6, output = listprocedure, method = taylorseries);
%;
Error, (in Shoot:-shoot) invalid boundary conditions, must be given at one point
 

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###############

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