Matlab ode45 Tutorial Part 2A: Multidimensional Problems

Hey guys. Welcome to the second part of my tutorial on Matlab's numerical ode solver. I actually decided to split this into a few subsections to keep videos at a reasonable length. This is part one of these videos, and it introduces you to the idea of handling Matlab's ode solver with multi-dimensional problems. Although you'll only see 2D examples here, note that the information shown applies to systems of any dimension. Also remember that the rules given here for ode45 also apply to Matlab's other numerical ode solvers.
Part 2B (Second Physical Example):
• Matlab ode45 Tutorial ...
Part 2C (A Faster Approach with Matrices):
• Matlab ode45 Tutorial ...
I want to give my sincerest thanks to the legendary Professor Vincent Nguyen at the University of Maryland, College Park. Without his help, I would never be able to understand how to use Matlab's ode solver like I do today.

[@anthonyheak3479]

Great video, thanks!

[@surajkumarm2215]

The best explanation! Thank you...

[@mohanadsayedoraby7534]

Wonderful explanation. Thank you very much.

[@lucasg8417]

Thanks for these videos! Helped me solve the differential equations for a 3 DOF planar RRR robot for animation purposes. -Cheers

[@mishalmohanlal2096]

Nice videos! I use Octave instead of Matlab though...

[@jaylive99]

This is so f'n nice.. Thanx a bunch!! :D

[@eoghanoneill5458]

These videos are tremendous

[@TaterBot1000]

Thanks! Glad to be of assistance.

[@prasannakumar5691]

good explanation.. thank you

[@TaterBot1000]

Thanks! I'm glad it helped

[@bronktug2446]

Hi, what do you do if the state vector contains matrix terms like a mass or stiffness matrix?

[@ash11591]

Hey how would the state variable matrix [s] look for an equation like x''+a(x'-y')+b(x-y) =0 n=i+j+k=2+1=3 s1=x s1'=x' s2=x' s2'=x'' s3=y s3'=y' But i have only one equation, so how do I determine the value of y'? Should i use an extra term s4=y' s4'=y'' ?

[@TaterBot1000]

Hi Ashlesh. You did a great job setting up the problem! Unfortunately, if you have two different functions that you're solving for (in this case x and y), then you'll need 2 equations to get a solution. Alternatively, you'd have to know one of the functions to get a solution. (ie., you'd need to know y to solve for x or vice versa.) That equation reminds me of the Base Excitation problem in Vibrations. Is there somewhere that your problem is specifically coming from? And were you given any additional information for your problem?

[@lahbibbenahmadi3955]

Thank you very much for the best explation, I need your help please if possible I the extract individual values part when I write ( x = state_values(:1);) I get this message : Invalid syntax at '1' I use all your steps but I stopped in this problem if you want to share the code to verify I will , thank you very much

[@ShareInfos516]

You need a semi colon right before 1, x = state_values(: ,1);

[@elewojo]

It keeps telling me that s needs to be defined.

[@TaterBot1000]

Hmmm. Can you show me what code you have? Also what version of Matlab are you using?