Handle URI:
http://hdl.handle.net/10754/599473
Title:
Rectangular spectral collocation
Authors:
Driscoll, Tobin A.; Hale, Nicholas
Abstract:
Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.
Citation:
Driscoll TA, Hale N (2015) Rectangular spectral collocation. IMA J Numer Anal: dru062. Available: http://dx.doi.org/10.1093/imanum/dru062.
Publisher:
Oxford University Press (OUP)
Journal:
IMA Journal of Numerical Analysis
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
6-Feb-2015
DOI:
10.1093/imanum/dru062
Type:
Article
ISSN:
0272-4979; 1464-3642
Sponsors:
This work was supported by The MathWorks, Inc. and by King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDriscoll, Tobin A.en
dc.contributor.authorHale, Nicholasen
dc.date.accessioned2016-02-28T05:51:47Zen
dc.date.available2016-02-28T05:51:47Zen
dc.date.issued2015-02-06en
dc.identifier.citationDriscoll TA, Hale N (2015) Rectangular spectral collocation. IMA J Numer Anal: dru062. Available: http://dx.doi.org/10.1093/imanum/dru062.en
dc.identifier.issn0272-4979en
dc.identifier.issn1464-3642en
dc.identifier.doi10.1093/imanum/dru062en
dc.identifier.urihttp://hdl.handle.net/10754/599473en
dc.description.abstractBoundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.en
dc.description.sponsorshipThis work was supported by The MathWorks, Inc. and by King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.en
dc.publisherOxford University Press (OUP)en
dc.titleRectangular spectral collocationen
dc.typeArticleen
dc.identifier.journalIMA Journal of Numerical Analysisen
dc.contributor.institutionDepartment of Mathematical Sciences, University of Delaware, Newark, DE 19716, USAen
kaust.grant.numberKUK-C1-013-04en
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