Author
Trefethen, L
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
Favourite
Off
Publication type
Journal Article
Publication date
07 May 2020
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