Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0
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 analysi...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2020
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| _version_ | 1797092639326076928 |
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| author | Trefethen, LN |
| author_facet | Trefethen, LN |
| author_sort | Trefethen, LN |
| collection | OXFORD |
| description | 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). |
| first_indexed | 2024-03-07T03:48:52Z |
| format | Journal article |
| id | oxford-uuid:c0830903-95ca-4e08-95e4-384390c64ce7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:48:52Z |
| publishDate | 2020 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:c0830903-95ca-4e08-95e4-384390c64ce72022-03-27T05:54:57ZEight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c0830903-95ca-4e08-95e4-384390c64ce7EnglishSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2020Trefethen, LNBoundary-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). |
| spellingShingle | Trefethen, LN Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title | Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title_full | Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title_fullStr | Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title_full_unstemmed | Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title_short | Eight perspectives on the exponentially ill-conditioned equation εy'' − xy' + y = 0 |
| title_sort | eight perspectives on the exponentially ill conditioned equation εy xy y 0 |
| work_keys_str_mv | AT trefethenln eightperspectivesontheexponentiallyillconditionedequationeyxyy0 |