I agree that the choice on Matlab is bvp4c or bvp5c. However, if your boundary value problem is in a high order form (i.e. the states are in cascade), scilab has the bvode based on Ascher et al fortran routines and that we have successfully used in the following references. 

More precisely, if your are solving an optimal control problem and if your dynamics are in normal form, the the adjoint states have a dual normal form and the boundary value problem is in n-th order form. In this case, bvode is faster and more accurate.

Inversion in indirect optimal control: constrained and unconstrained cases

Inversion in indirect optimal control of multivariable systems

I highly recommend Asher's book

François

http://www.amazon.com/Numerical-Solution-Differential-Equations-Mathematics/dp/0898713544/ref=sr_1_1?ie=UTF8&qid=1410250236&sr=8-1&keywords=ascher+boundary+value+problems

Article Inversion in indirect optimal control of multivariable systems

Conference Paper Inversion in indirect optimal control: Constrained and uncon...

Hello,

Here is the link of Matlab codes and examples to do that;

http://www.mathworks.com/help/matlab/ref/bvp4c.html

Thanks.

Hello you can use an iterative, called also shooting method.

http://www.mathworks.se/matlabcentral/fileexchange/32451-shooting-method

If your bvp problem is related to an optimal control problem, you may have a look at the BOCOP toolbox: http://bocop.org

BOCOP uses a direct method combining discretization and interior point

methods.

More in for here:

Bonnans, F.J., Martinon, P., Grelard, V.: Bocop - A collection of examples. Tech. rep., INRIA (2012). http://hal.inria.fr/hal-00726992. RR-8053

Best,

Mickael

bvp4c -

Solve boundary value problems (BVPs) for ordinary differential equations

I agree that the choice on Matlab is bvp4c or bvp5c. However, if your boundary value problem is in a high order form (i.e. the states are in cascade), scilab has the bvode based on Ascher et al fortran routines and that we have successfully used in the following references. 

More precisely, if your are solving an optimal control problem and if your dynamics are in normal form, the the adjoint states have a dual normal form and the boundary value problem is in n-th order form. In this case, bvode is faster and more accurate.

Inversion in indirect optimal control: constrained and unconstrained cases

Inversion in indirect optimal control of multivariable systems

I highly recommend Asher's book

François

http://www.amazon.com/Numerical-Solution-Differential-Equations-Mathematics/dp/0898713544/ref=sr_1_1?ie=UTF8&qid=1410250236&sr=8-1&keywords=ascher+boundary+value+problems

Article Inversion in indirect optimal control of multivariable systems

Conference Paper Inversion in indirect optimal control: Constrained and uncon...

To solve linear or non-linear ordinary differential equations, one can use MATLAB built-in solver bvp4c and bvp5c.