I have attached a PDF of how one might solve M. A. Sadiq's BVP using a Shooting method. The coding is done in Mathematica and takes about 5 lines of code to solve and plot the solution.

If you're going to use Matlab, why not just use one of Matlab's built in ODE integrators? There are a number, of various accuracy and ability to handle stiff problems. See the link below, which is an index of these.

http://www.mathworks.com/help/matlab/ordinary-differential-equations.html

See for example "Numerical Methods for Engineers and Scientists", Second Ed. Joe D. Hoffman - chapter 8.

As noted by Carl Matlab (like Mathematica which I am more familiar with) have excellent ODE integrators(solvers) when the problem is formulated as an initial value problem. To handle nonlinear boundary value problems you have several options. Solve the problem using a finite difference/Finite element method or spectral method and thereby reduce the problem to a system of nonlinear algebraic equations which can be solved with Newton's method. Matlab and Mathematica have Newton solvers as well.

An alternative method is to make use of the ODE solvers but reformulate your problem as an initial value problem (with an unknown initial value) and then write your own shooting method so that the BC at the other end is satisfied. This feature in also built into Mathematica's NDSolve function ( and likewise I suspect in Matlab)., but its reliability is not as great because nonlinear BVP can be very stiff and finding a suitable guess for the unknown IC in the shooting method can be problematic. So writing your own shooting method sometimes is the best option.

If you are interested in how such problems can be programmed on Mathematica you can visit my site: http://www.ekayasolutions.com/UCDMath/FluidMechanics.php

and download the flow over a rotating disk problem ( Both PDF and Mathematica notebook files are available for download. There are other examples on this website.

I should also note as Diego mentioned , shooting methods are also discussed in most introductory Numerical Methods textbooks.

Hello,

If you want to make your own code, I think shooting method is handy and programmable.

However, Finite Difference method is easy to use, but it has an area for stability to consider.

And if you want to use MATLAB toolbox, the 'bvp' function can solve the problem,

If you write down your equation here, I can suggest more specific.

Here is the file include equations

I think you can use bvp function to solve it, but you may have to allocate a very great number instead of infinity.

An alternative option could be to use a mapping (for instance in the form s = x/sqrt(1-x^2)), and solve your problem in s in [0,1). This may pose, however, additional challenges after applying the chain rule to your derivatives (like indefinite Jacobians, etc.) when s tends to 1, but might be worth trying.

I have attached a PDF of how one might solve M. A. Sadiq's BVP using a Shooting method. The coding is done in Mathematica and takes about 5 lines of code to solve and plot the solution.

you can use maple rk 4-5, or you can build your own code using matlab/scilab using FEM or shooting method

i think bvp4c MATLAB function very helpful for u

Built in Matlab solver bvp4c is handful.