A Spectral Method for the Eigenvalue Problem for Elliptic Equations

Abstract

Let $\Omega$ be an open, simply connected, and bounded region in ${\mathbb{R}}^d$, $d\ge 2$, and assume its boundary $\partial \Omega$ is smooth. Consider solving the eigenvalue problem $Lu=\lambda u$ for an elliptic partial differential operator $L$ over $\Omega$ with zero values for either Dirichlet or Neumann boundary conditions. We propose, analyze, and illustrate a 'spectral method' for solving numerically such an eigenvalue problem. This is an extension of the methods presented earlier in [5],[6].

28 pages, 13 figures

References in corpus (2)

• A Spectral Method for Elliptic Equations: The Neumann Problem
• A spectral method for elliptic equations: the Dirichlet problem

Cited by in corpus (4)

• Creating domain mappings
• A Spectral Method for Nonlinear Elliptic Equations
• Evaluating Polynomials Over the Unit Disk and the Unit Ball
• Reproducing Kernels of Sobolev Spaces via a Green Kernel Approach with Differential Operators and Boundary Operators