Superconvergent interpolants for collocation methods applied to mixed-order BVODEs

Citation
Wh. Enright et R. Sivasothinathan, Superconvergent interpolants for collocation methods applied to mixed-order BVODEs, ACM T MATH, 26(3), 2000, pp. 323-351
Citations number
14
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Science & Engineering
Journal title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN journal
0098-3500 → ACNP
Volume
26
Issue
3
Year of publication
2000
Pages
323 - 351
Database
ISI
SICI code
0098-3500(200009)26:3<323:SIFCMA>2.0.ZU;2-#
Abstract
Continuous approximations to boundary value problems in ordinary differenti al equations (BVODEs), constructed using collocation at Gauss points, are m ore accurate at the mesh points than at off-mesh points. From these approxi mations, it is possible to construct improved continuous approximations by extending the high accuracy that is available at the mesh points to off-mes h paints. One possibility is the bootstrap approach, which improves the acc uracy of the approximate solution at the off-mesh points in a sequence of s teps until the accuracy at the mesh points and off-mesh points is consisten t. A bootstrap approach for systems of mixed-order BVODEs is developed to i mprove approximate solutions produced by COLNEW, a Gauss-collocation-based software package. An implementation of this approach is discussed and numer ical results presented which confirm that the improved approximations satis fy the predicted error bounds and are relatively inexpensive to construct.