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Differential Eigensystems

Differential Eigensystems in Mathematica 11

Mathematica Version 11 extends its symbolic and numerical differential equation-solving capabilities to include finding eigenvalues and eigenfunctions over regions. Given a possibly coupled partial differential equation (PDE), a region specification, and, optionally, boundary conditions, the eigensolvers find corresponding eigenvalues and eigenfunctions of the PDE operator over the given domain. This functionality will enable you to gain a deeper understanding of your physics and engineering designs.

Key Features

  • Find symbolic eigenvalues and eigenfunctions over regions. »
  • Find numeric eigenvalues and eigenfunctions over regions. »
  • Find eigenvalues and eigenfunctions of PDEs with arbitrary-order time derivative.
  • Specify and solve eigenvalue problems in one, two, and three dimensions.
  • Specify and solve constrained or unconstrained eigenvalue problems. »
  • Freely formulate coupled PDEs for multi-physics eigenvalue analysis. »
  • Specify domains using the full geometric region framework. »
  • Use automatically generated meshes with curved boundaries for numeric eigenvalue computations. »

Related Examples


A Laplacian's Eigenvalues & Eigenfunctions »
Solve the Eigenproblem of a Constrained Laplacian »
Find the Spectrum of a Schrödinger Operator »
Probe the Eigenproblem of a Wave Operator »

Analyze a Sturm–Liouville Operator with an Asymmetric Potential  »
Study a Sturm–Liouville System with Antiperiodic Boundary Conditions  »
Investigate a Laplace Equation on a Torus  »
Compute Eigenfunctions for a Clamped Membrane  »

Compute Eigenfunctions in an L-shaped Region »
Analyze the Acoustic Eigenmodes of a Car »
Compute the Spectrum on a Koch Snowflake »
Find Eigenvalues That Lie in an Interval  »

Find Aharonov–Bohm Eigenvalues  »
Eigenfunctions of a 3D Laplacian »
Eigenmodes in a Knot »
A Crankshaft's Eigenvalues and Eigenfunctions  »

Find a 1D Laplacian's Symbolic Eigenfunctions »
Compute Symbolic Eigenvalues »
Model Small Oscillations in a CO Molecule »
Generate an Eigenfunction Expansion  »

Calculate Exact Eigenfunctions for the Laplacian in a Rectangle »
Obtain a Clamped Triangular Membrane's Symbolic Eigenfunctions »
Compute the Exact Eigenmodes of the Heat Equation »
Create a Gallery of Eigenfunctions for the Laplacian in a Ball »