Rectangular spectral collocation

Tobin A. Driscoll, Nicholas Hale

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)dru062
JournalIMA Journal of Numerical Analysis
Issue number1
StatePublished - Feb 6 2015
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This work was supported by The MathWorks, Inc. and by King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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