Dear all
I have two region and one ODE, I can't use Heaviside to model the thickness variation so I have to solve this ODE separately in two region, the original problem is BVP but now I face to two IVP and additional condition in the border of two region, so what should I do?
The statement of the problem which you wish to solve is incomplete. It is also necessary to give some form of continuity conditions relating dF1/dR and dF2/dR at R=R2.
Your problem could be solved as a two point boundary value problem where the initial value of dF1/dR at R=R1 is unknown, but has to be iterated upon so that F2(R3)=P2 is satisfied. The only difficulty will be the making sure that once your code has integrated as far as R=R2, and has calculated the values of F1 and dF1/dR at that point, that the correct values of F2 and dF2/dR are then defined so that the rest of the computation from R2 to R3 is undertaken.
I don't know how easy it is to persuade matlab to do this, but it is fairly straightforward with one's own self-written Fortran code.
I think that it is also possible to write down the general solution of this problem in integral form. This might be the better way to go.
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