I attached my program. It is a problem of solving 6 third-order ODEs with 18 boundary conditions. After using NDSolve to get the numerical solutions of the problem, I plotted the first and second derivatives. I believe that the graphs of the first and second derivatives are wrong, since they are totally different from what I expected. Besides, in the boundary conditions, there is one stipulating that u2a''[1/2]==0. But after I extracted the results, I got u2a''[1/2]==-0.614559. So there is definitely something wrong, either with my code or with the algorithm of NDSolve. I don't know where the problem is. Could anyone help me? Many thanks!!
This is a boundary value problem, not a initial value problem. Actually, function u2a[x] is defined on 1/2=<x<=1, and u6b[x] is defined on 1=<x<=3/2, so there cannot be u2a' and u6b. I don't think there is anything wrong with my boundary conditions, since I wrote them according to the basic principles of mechanics, although I could not guarantee that they are 100% correct. Anyway, many thanks for your reply and help!
I used "method of Lines" and it helped.I found a website that can help you solve the problem.I hope. LINK
See file Attachment.
Many thanks for your help! After thinking it over, I feel that maybe I did give some wrong boundary conditions...Sorry for the time you spend on this problem...Once again, many thanks.
u2b' = 0 and u2b'[1/2] = u2a'[1/2]
Here is a mistake. Initial condition he can not have two values and forgot u6b[?]==?.
so u2b' = 0 ,u2b' = u2a' and e.g u6b=0