NDEigensystem

NDEigensystem[ℒ[u[x, y, ...]], u, {x, y, ...} ∈ Ω, n] gives the n smallest magnitude eigenvalues and eigenfunctions for the linear differential operator ℒ over the region Ω.

Examples

Eigenvalues of Laplacian on a disk:

{vals, funs} = NDEigensystem[{-Laplacian[u[x, y], {x, y}], 
  DirichletCondition[u[x, y] == 0, True]}, u, {x, y} ∈ Disk[], 3]

Please visit the official Wolfram Language Reference for more details.