Wolfram Language

Partial Differential Equations

Solve PDEs with Complex-Valued Boundary Conditions over a Region

Solve a Laplace equation with a complex-valued boundary condition.

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Click for copyable input
ifun = NDSolveValue[{-\!\( \*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[x, y]\)\) == 1 + NeumannValue[I, x < 0], DirichletCondition[u[x, y] == 0, x > -0]}, u, {x, y} \[Element] Disk[]]
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Visualize the result.

In[2]:=
Click for copyable input
Plot3D[{Re[ifun[x, y]], Im[ifun[x, y]]}, {x, y} \[Element] Disk[], PlotTheme -> "Detailed"]
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