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Mathematics of Computation

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Eigenvalue problems on infinite intervals

Author: Peter A. Markowich
Journal: Math. Comp. 39 (1982), 421-441
MSC: Primary 34B25
MathSciNet review: 669637
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Abstract: This paper is concerned with eigenvalue problems for boundary value problems of ordinary differential equations posed on an infinite interval. Problems of that kind occur for example in fluid mechanics when the stability of laminar flows is investigated. Characterizations of eigenvalues and spectral subspaces are given, and the convergence of approximating problems, which are derived by reducing the infinite interval to a finite but large one and by imposing additional boundary conditions at the far end, is proved. Exponential convergence is shown for a large class of problems.

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Keywords: Boundary value problems of linear equations, spectral theory of boundary value problems, boundedness of solutions, asymptotic expansion, theoretical approximation of solutions
Article copyright: © Copyright 1982 American Mathematical Society