Boundary value problem with singularity using bvp4c

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Isaac Paten
Isaac Paten 2021-8-7
评论： Isaac Paten 2021-8-10
I am attempting to solve a boundary value problem with a singularity on one of the boundaries.
The ODEs in the system that I am solving are all of the following form:
Defined in the interval
With boundary conditions:
At the boundary, the term becomes 0/0. I am aware that bvp4c can solve problems with a singularity that has the form as x→0, but since my singularity is in the form I'm not sure if bvp4c will be appropriate.
Currently, the code does solve using bvp4c, and produces the figure that I have attached. As can be seen in the figure, my problem is that the value of is forced to 0 at the boundary where . Instead, I want to be able to evaluate the limit that is tending to.
My questions are:
1) Is it possible to evaluate the limit of as x→?
2) Is bvp4c suitable for this problem? If not, would someone be able to recommend a different function? I have had a look sbvp, but I do not think the type of singularities dealt with in this function are applicable either.
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David Goodmanson
David Goodmanson 2021-8-9
Hi Isaac,
could you post all three equations and all the boundary conditions?
Isaac Paten
Isaac Paten 2021-8-10
Hi David,
I think I might have oversimplified my problem by trying to make my question clear. There are an extra 3 equations which I did not mention - my apologies. I have included all equations and boundary conditions below.
The equations for y:
The equations describing q, which I did not mention before:
The equations for qtot and ytot are:
All boundary conditions are:
When x=0:
When x=1.5:
All constants are given below:
Sorry for any confusion caused. Thanks again in advance.
Best,
Isaac

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