Matlab: Solving Boundary Value Problems

This video describes how to solve boundary value problems in Matlab, using the bvp4c routine. A full res version can be found at http://blanchard.ep.wisc.edu These videos were recorded for a course I teach as part of a distance masters degree. See http://mepp.engr.wisc.edu

Category:

Science & Technology

Tags:

• matlab
• numerical
• differential
• equation

[MsChano87]

Hi Mr.Jakeblanchard,

I have a query to ask in matlab which i hope you can help with. I have some 50 images which i want to stack along the Z direction at a fixed interval between the images/slices i.e. images are parallel to X-Y plane. After stacking I want to develop a 3D image by using some kind of interpolation between the slices. Is this possible to do in matlab??. If possible can you shed some light on what lines should I proceed??

Thankyou for your time!!!

[jakeblanchard]

@MsChano87

I have no idea if this is possible. Sorry.

[fgiuglia]

Thanks for the very useful video. I can't understand how can I find the guess of my bvp.. could you help me? and how did you choose yours?

[jakeblanchard]

@fgiuglia

I try not to solve a problem numerically until I have a pretty good idea what the answer should look like. The best approach is to work out some kind of approximate analytical solution. Then this can be used as an initial guess for the numerical solution.

[fgiuglia]

@jakeblanchard

Thank you very much. Sorry if I am not smart, but what is the link with the constants in the initial guess and your solution?

[jakeblanchard]

@fgiuglia

I knew the analytical solution for my problem, so it was pretty easy to formulate a rough guess. Also, this is a linear equation so the guess is relatively unimportant. Guesses are much more important for nonlinear equations.

I'll repeat, if you are going to solve a problem numerically, you should already know what the solution looks like. Use approximations to allow for analytical solutions of a simplified problem. Then you can use this approximation for the guess.

[jakeblanchard]

@jakeblanchard

One more suggestion. The first time you use a tool like bvp4c, test it on a problem for which you know the exact solution. Then you can be sure you're using the tool correctly. Then you can move on to solve harder problems for which you don't have an analytical solution.

[fgiuglia]

@jakeblanchard thank you, I will try to manage it!

[fgiuglia]

Thanks for the very useful video. I can't understand how can I find the guess of my bvp.. could you help me? 

[jakeblanchard]

@uoweme5grand

It could be you need a better initial guess. It also might be a problem with the equations themselves. I'd have to see the code to be sure. You can send me the code if you want me to look at it. Send to blanchard "at" engr.wisc.edu