Boundary value problem with singularity using bvp4c

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.

[David Goodmanson]

Hi Isaac,

you only show an ode for f, so is g a known function?

[Isaac Paten]

Hi David,

Thanks for the comment. Yes g is a known function. I am trying to solve 3 coupled ODEs (all in the form shown above). If the variables in each equation were y1, y2, and y3, then g=y1+y2+y3.

Best,

Isaac

[David Goodmanson]

Hi Isaac,

could you post all three equations and all the boundary conditions?

[Isaac Paten]

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