Rectangular spectral collocation

Type
Article

Authors
Driscoll, Tobin A.
Hale, Nicholas

KAUST Grant Number
KUK-C1-013-04

Date
2015-02-06

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.

Acknowledgements
This work was supported by The MathWorks, Inc. and by King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.

Publisher
Oxford University Press (OUP)

Journal
IMA Journal of Numerical Analysis

DOI
10.1093/imanum/dru062

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