Verified numerical computations for an inverse elliptic eigenvalue problem with finite data

2001 ◽  
Vol 18 (2) ◽  
pp. 587-602 ◽  
Author(s):  
Mitsuhiro T. Nakao ◽  
Yoshitaka Watanabe ◽  
Nobito Yamamoto
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Computations ◽  
Elliptic Eigenvalue Problem ◽  
Finite Data

A two parameter eigenvalue problem

1974 ◽  
Vol 10 (1) ◽  
pp. 39-50
Author(s):  
J.A. Rickard
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Order Differential Equation ◽  
Inviscid Fluid ◽  
Free Oscillations ◽  
Numerical Computations ◽  
Second Order Differential Equation ◽  
Independent Variable ◽  
Two Parameters ◽  
Two Parameter

An ordinary second order differential equation is considered in which the coefficients are dependent on two parameters ω and F as well as the independent variable μ. The equation arises in the study of free oscillations of incompressible inviscid fluid in global shells. An asymptotic technique is presented which estimates the eigenvaiues (that is the values of ω for which the solution is bounded for all |μ| ≤ 1) as functions of F, as F → ∞. The agreement of the results with numerical computations is also discussed.

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