Brown, B. Malcolm and Langer, M. and Marletta, M. and Tretter, C. and Wagenhofer, M. (2010) Eigenvalue enclosures and exclosures for nonselfadjoint problems in hydrodynamics. LMS Journal of Computation and Mathematics, 13. pp. 6581. ISSN 14611570

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Abstract
In this paper we present computerassisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for nonselfadjoint boundary eigenvalue problems, the eigenvalues of which are highly sensitive to perturbations. We apply the algorithm to: the OrrSommerfeld equation with Poiseuille profile to prove the existence of an eigenvalue in the classically unstable region for Reynolds number R=5772.221818; the OrrSommerfeld equation with Couette profile to prove upper bounds for the imaginary parts of all eigenvalues for fixed R and wave number α; the problem of natural oscillations of an incompressible inviscid fluid in the neighbourhood of an elliptical flow to obtain information about the unstable part of the spectrum off the imaginary axis; Squire's problem from hydrodynamics; and resonances of onedimensional Schrödinger operators.
Item type:  Article 

ID code:  25773 
Keywords:  eigenvalue , enclosures, exclosures, hydrodynamics, Mathematics, Mathematics(all), Computational Theory and Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  05 Jul 2010 10:55 
Last modified:  21 May 2015 12:35 
URI:  http://strathprints.strath.ac.uk/id/eprint/25773 
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