BVP for system of 2 second order ODEs

Question

e_frog 2020-11-3

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https://ww2.mathworks.cn/matlabcentral/answers/634784-bvp-for-system-of-2-second-order-odes

回答： Alan Stevens 2020-11-3

I have a system of two second order ODEs that I want to calculate using bvp4c. I have some problems transforming the second order ODEs in acceptable first order problems and then setting up the boundary conditions. Help is very much appreciated!

My system of equations with

and

:

where

,

and h are known constant values and

is a known linear function.

The boundary conditions are:

,

I have some problems setting this up, because

and

are appearing in both ODEs.

Thanks in advance!

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Answer 1

Alan Stevens 2020-11-3

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Here is how you can express your second order equations as first order ones

You should now be able to express your boundary conditions ok, though you seem to have too many! You have four initial conditions which should be enough to determine your dependent variables.