Wolfram Language & System 10.3 (2015)|Legacy Documentation

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DEigenvalues

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

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

Details and OptionsDetails and Options

  • DEigenvalues can compute eigenvalues for ordinary and partial differential operators with given boundary conditions.
  • DEigenvalues gives a list of the n smallest magnitude eigenvalues .
  • An eigenvalue and eigenfunction pair for the differential operator satisfy .
  • 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[DEigenvalues[]] calls NDEigenvalues for eigenvalues that cannot be computed symbolically.
  • The Assumptions option can be used to specify assumptions on parameters.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Find the 4 smallest eigenvalues of the Laplacian operator on :

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

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Introduced in 2015
(10.3)