Report Number: CS-TR-69-121
Institution: Stanford University, Department of Computer Science
Title: Accurate bounds for the eigenvalues of the Laplacian and applications to rhombical domains
Author: Moler, Cleve B.
Date: February 1969
Abstract: We deal with the eigenvalues and eigenfunctions of Laplace's differential operator on a bounded two-dimensional domain G with zero values on the boundary. The paper describes a new technique for determining the coefficients in the expansion of an eigenfunction in terms of particular eigenfunctions of the differential operator. The coefficients are chosen to make the sum of the expansion come close to satisfying the boundary conditions. As an example, the eigenvalues and eigenfunctions are determined for a rhombical membrane.