bvpinit giving wrong behavior!
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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.
. 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):
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!
) 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.
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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2022 年 4 月 6 日
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