Boundary value problem-bvp4c

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sepideh 2023-7-3

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https://ww2.mathworks.cn/matlabcentral/answers/1991218-boundary-value-problem-bvp4c

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 :

采纳的回答

Torsten 2023-7-3

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1991218-boundary-value-problem-bvp4c#answer_1266393

Use ode45 and integrate backwards:

https://uk.mathworks.com/matlabcentral/answers/1881197-numerical-integration-backwards-for-ode45

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 2023-9-11