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PDE solver with variables at different points
Posted Aug 14, 2014, 10:50 a.m. EDT Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.3, Version 4.3a, Version 4.3b, Version 4.4 3 Replies
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I am trying to solve a PDE where two terms contain variables at different points, something such as:
u"(x) + u'(L-x)=f(x)
This is a sample though, maybe there is no solution to this, but my point is how we can use the function u(x) at different points? The model is 1D with length equal to L.
I appreciate any help,
Best,
Hossein
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That's a non-local PDE. I think on something like this:
f-comp1.at1(L-x,ut)
to be written in the source term of your coefficient-form PDE (of course, you only have to set the term in utt). Note that I have used 'spatial at' operator for dimension 1 (the example you give). Of course, ut is the derivative of u with respect to time at that point.
But I'm not sure if it does what you want, please check if you think it can work.
If that does not work, perhaps you could integrate (in x) twice, and compute the non-local integral of u(L-x) easily by means of integration operator.
Bye.
Jesus.
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f=utt-at1(L-x,ut)
'at1(coordinate,expression)' evaluates 'expression' at 'coordinate' in a 1D model. There are similar at2 and at3 functions for 2D and 3D models.
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