Shooting method for solving 3rd Oder ODE with RK method

This is my 3rd Order IVP. D[y[x], {x, 3}] == (m/2)*((D[y[x], x])^2 - 1) - ((m + 1)/2)* y*(D[y[x], {x, 2}])^2. Initial conditions given are as follows y[0] = 0; y'[0] = 0; y''[0] = 1; (* This is the First assumed value of y''[0] for initializing shooting method using RK 4rth order method *) 

For this problem y'[infinity] is equal to 1, I want to loop the shooting method using Runge Kutta 4 th order method in such a way that after calculations, it will check the y'[] value at sufficiently large value of x and from experimental results, for x ~ 7-8, f'[] is 1.

To Use RK method I redefined the equation like

D[l[x], {x, 2}] ==  z; D[y[x], x] ==  l; D[z[x], x] == (m/2)*(l^2 - 1) - ((m + 1)/2)*z*y;


Now I could write one loop for RK method but this is proving out a bit tough for me because I have to generate a list for different values of f[0] { 0,1} and m is also a variable with range (0-1) step size 0.01 & then I have to deal with 3 equations simultaneously. I am solving this over C programming but its not that efficient. I dont know how to go ahead. If anyone could throw some light.....

• Where's the definition of m? Then your equation involves simple mistake, y*(D[y[x], {x, 2}])^2 should be y[x] (D[y[x], {x, 2}])^2. Finally, I tried to set m = 1, and this equation is easily solved by NDSolve. Commented Mar 3, 2014 at 2:17
• Have there been some recent homework assignments on the shooting method? Seems to have been a few related questions recently. Is this a homework problem? Commented Mar 3, 2014 at 4:17
• @xzczd- How could you solve this ODE with NDsolve. What you assumed the value of f''[0]. Since we only know f[0] and f'[0]. We do know f'[infinity]= 1 but we cant use this condition in NDSolve, that's why we have to use shooting method I guess. m is a list you can assume - {0.1,0.2,0.3...........1.0}. f[0] is same list. I wish to make a Module function which takes these euqation, perform RK method over them and solved and plot the results for different m and f[0]. Commented Mar 3, 2014 at 6:02
• @MikeHoneychurch- I dont know about any homework but this a problem related to Boundary layer flow with Wedge effect and Blowing and suction together. Commented Mar 3, 2014 at 6:03
• @MikeHoneychurch this also is applied as an approximation method in quantum chemistry. It converges slowly. Commented Mar 3, 2014 at 6:30