Boundary value problem-bvp4c

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sepideh
sepideh 2023-7-3
评论： sepideh 2023-9-11
Hello
I am working on a paper by Di Federico et al 2012, they solved this by Mathematica@. I need to reproduce it in MATLAB and extend it for radial geometry.
Here is the problem :
I am trying to solve an ODE ( has been derived from an PDE by scaling and similarity solution process) which I have two values of it at the end of the interval [0,1] .
I know that as , the function tends to zero .
Also I know that as the derivative equals to .
as "bvp4c" needs the values in two different point, how should I write the residual function "bcfun" for this problem as I do not have two points ?
instead I have information about one end point and the slope near that point
This is the system of first order ODE :
also there is singularity near this point which they handle it by studying the problem in the neighborhood
the solution should have an answer like this :

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Torsten
Torsten 2023-7-3
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Torsten
Torsten 2023-9-11
Yo divide by x and y(1). Thus you have to start with something small and different from 0 for y(1) in the y0-vector and you must integrate up to something small and different from 0 for xspan(2) in the xspan-vector.
sepideh
sepideh 2023-9-11
thanks. now they are match

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