Lamé's formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition. They are shown to form a complete orthonormal system. Various properties of the spectrum and modal functions are explored. 1. Introduction. The eigenstructure… (More)
Lamé's formulas for the eigenvalues and eigenfunctions of the continuous Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the discrete Laplacian.
We examine the eigenstructure of generalized isosceles triangles and explore the possibilities of analytic solutions to the general eigenvalue problem in other triangles. Starting with work based off of Brian McCartin's paper on equilateral triangles, we first explore the existence of analytic solutions within the space of all isosceles triangles. We find… (More)
Hikari Ltd is a publisher of international scientific journals and books. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the publisher Hikari Ltd. for all of the sacrifices that they made for their children. Preface v PREFACE In Lord Rayleigh's… (More)