Wolfram Language & System 11.0 (2016)|Legacy Documentation

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DEigensystem

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

DEigensystem[eqns,u,t,{x,y,}Ω,n]
gives the eigenvalues and eigenfunctions for solutions u of the time-dependent differential equations eqns.

Details and OptionsDetails and Options

  • DEigensystem can compute eigenvalues and eigenfunctions for ordinary and partial differential operators with given boundary conditions.
  • DEigensystem gives lists {{λ1,,λn},{u1,,un}} of eigenvalues λi and eigenfunctions ui.
  • An eigenvalue and eigenfunction pair {λi,ui} for the differential operator satisfy [ui[x,y,]]==λi ui[x,y,].
  • Homogeneous DirichletCondition or NeumannValue boundary conditions may be included. Inhomogeneous boundary conditions will be replaced with corresponding homogeneous boundary conditions.
  • When no boundary condition is specified on the boundary Ω, then this is equivalent to specifying a Neumann 0 condition.
  • The equations eqns are specified as in DSolve.
  • N[DEigensystem[]] calls NDEigensystem for eigensystems that cannot be computed symbolically.
  • The following options can be given:
  • Assumptions$Assumptionsassumptions on parameters
    MethodAutomaticwhat method to use
  • Eigenfunctions are not automatically normalized. The setting Method->"Normalize" can be used to give normalized eigenfunctions.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the 4 smallest eigenvalues and eigenfunctions of the Laplacian operator on [0,π]:

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Visualize the eigenfunctions:

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Compute the first 6 eigenfunctions for a circular membrane with the edges clamped:

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Visualize the eigenfunctions:

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Introduced in 2015
(10.3)