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 Options

  • DEigenvalues can compute eigenvalues for ordinary and partial differential operators with given boundary conditions.
  • DEigenvalues gives a list {λ1,,λn} of the n smallest magnitude eigenvalues λi.
  • 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[DEigenvalues[]] calls NDEigenvalues for eigenvalues that cannot be computed symbolically.
  • The Assumptions option can be used to specify assumptions on parameters.

Examples

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Basic Examples  (2)

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

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

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Scope  (17)

Properties & Relations  (3)

Possible Issues  (2)

See Also

DEigensystem  DSolve  NDEigenvalues  Eigenvalues  DirichletCondition  NeumannValue

Introduced in 2015
(10.3)