Type
ArticleAuthors
Driscoll, Tobin A.Hale, Nicholas
KAUST Grant Number
KUK-C1-013-04Date
2015-02-06Permanent link to this record
http://hdl.handle.net/10754/599473
Metadata
Show full item recordAbstract
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.Sponsors
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)ae974a485f413a2113503eed53cd6c53
10.1093/imanum/dru062