Journal title
SIAM Review
DOI
10.1137/18M121232X
Issue
2
Volume
62
Last updated
2024-03-24T16:19:30.69+00:00
Page
439-462
Abstract
Boundary-value problems involving the linear differential equation $\varepsilon y'' - x y' + y = 0$ have surprising properties as $\varepsilon\to 0$. We examine this equation from eight points of view, showing how it sheds light on aspects of numerical analysis (backward error analysis and ill-conditioning), asymptotics (boundary layer analysis), dynamical systems (slow manifolds), ODE theory (Sturm--Liouville operators), spectral theory (eigenvalues and pseudospectra), sensitivity analysis (adjoints and SVD), physics (ghost solutions), and PDE theory (Lewy nonexistence).
Symplectic ID
957098
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Publication type
Journal Article
Publication date
07 May 2020