Dear All,
I am trying to solve a PDE in Mathematica, using the NDSolve function.
I want the solution that obeys some constraint. For example, I want the solution, say u(x,y), that satisfies integrate[u[x,y],{x,0,1}]==1.
How can I implement this constraint to the NDSolve?
I suggest you explore the use of WhenEvent function, which can be incorporated with NDSolve
see https://reference.wolfram.com/language/ref/WhenEvent.html.
There is an example using WhenEvent with a PDE
Try to consider a function v[x,y] such that v'x[x,y]=u[x,y], v[0,y]=0, v[1,y]=1 and to solve the system of PDE for u and v.
In addition to the helpful answers already given, there is a bit more to add.
An illustrative answer to this question is given at
https://groups.google.com/forum/#!topic/comp.soft-sys.math.mathematica/tl0g6PoFxBU
In addition, two answers to this question are given at
https://stackoverflow.com/questions/16981571/how-to-impose-a-constraints-in-the-ndsolve
The idea of the first example shared by James F. Peters is very impressive. But one comment is necessary. The line di=Plus@@((res/.t0)-reference)^2; must be replaced by di=Plus@@(((res/.t0)-reference)^2); because the program have to find the minimum of (fx(t)- reference[[1]])^2+ (fy(t)- reference[[2]])^2 rather than (fx(t)-reference[[1]]+ fy(t)- reference[[2]])^2. Of course, this remark is of secondary importance.
@ Victor J. Аdlucky :... one comment is necessary.
Many thanks for your incisive, very helpful suggestion. I will try it out.
An illustrative answer to this question is given at
https://groups.google.com/forum/#!topic/comp.soft-sys.math.mathematica/tl0g6PoFxBU
In addition, two answers to this question are given at
https://stackoverflow.com/questions/16981571/how-to-impose-a-constraints-in-the-ndsolve
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