I use MATLAB commands 'ode23' and 'ode45' for solving systems of differential equations and this program involves an *.m function (system), time-span and initial-condition (x0) only. How to solve BVPs in MATLAB? Can you give an example? Thank you!
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.
I suggest the introductory but rigorous book "Numerical Methods using Matlab" by G.Lindfield and J. Penny, chapters 5 and 6 (3rd edition).
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