| Summary: | 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).
|
|---|