Solution of a transcendental eigenvalue problem via interval analysis

A knowledge of the complex roots lambda of the transcendental eigenvalue eq uation sin lambda alpha = +/-lambda sin alpha is essential in the analysis of the slow viscous fluid flow in the neighbou rhood of a sharp corner which subtends an angle alpha is an element of (0,2 pi) to the fluid. Existing methods for finding all roots lambda essentiall y require an a priori knowledge of the solution structure; given that (lamb da(1), lambda(2),...,lambda(m)) are known, lambda(m+1) is determined via it erations, and/or a solution procedure initiated by lambda(m). We present he rein a general interval analysis method which exhaustively finds all roots lambda via only the original eigenvalue equation: no other information is r equired. The interval-analysis method automatically guarantees root existen ce and uniqueness while simultaneously providing error bounds. (C) 1999 Els evier Science Ltd. All rights reserved.