[問題]Poisson equation-numerical solutions
Consider the nonlinear Poisson equation for u=u(x,y) as follows:
u_xx+ u_yy = f(u) in {x,y | x^2+y^2<1}
x*u_x+y*u_y=0 on {x,y | x^2+y^2=1}
Here f(u) is a function which is implicit in u,
and f(u) cannot have an explicit function.
Moreover, by using NDSolve f(u) can be numerically plotted point by point.
Is it possible to use Mathematica to numerically solve
this boundary value problem? Thank you very much!
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