Solution of a transcendental eigenvalue problem via interval analysis

✍ Scribed by L.E Bateson; M.A Kelmanson; C Knudsen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 635 KB
• Volume: 38
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(99)00244-8

✦ Synopsis

Asina

is essential in the analysis of the slow viscous fluid flow in the neighbourhood of a sharp corner which subtends an angle a E (0, 2~r] to the fluid. Existing methods for finding all roots A essentially require an a priori knowledge of the solution structure; given that {A1, A2,..., Am} are known, Am+l is determined via iterations, and/or a solution procedure initiated by Am. We present herein a general interval analysis method which exhaustively finds all roots A via only the original eigenvalue equation: no other information is required. The interval-analysis method automatically guarantees root existence and uniqueness while simultaneously providing error bounds.