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bvpinit giving wrong behavior!

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Marcus Rosales
Marcus Rosales 2022-4-6
关闭： Marcus Rosales 2022-4-6
I'm tryping to solve the following nonlinear Diff. Eq:
, using the function bvp4c and the boundary conditions: . After finding α, I need to use and to model something. Also, t is used to help simplify the math, but it is related to distance r via: . Here, is just some characteristic length scale for the system.
The issue is I expect linear behavior for around (being ) since α will be small here. This can be seen by realizing continuity of α and our boundary condition on the left implies this. Indeed, our differential equation reduces to (near this point):
The plot I have included (r ) illustrates the behavior is quadartic near ... I can not figure out exactly why!
I included my code and setup as well. The only reason I can see something may go wrong is I mapped to using tanh. I tried running bvp4c with something big, so I could still treat it numerically, but no luck... I kept getting a singular Jacobian.
Any help will be greatly appreciated!

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