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    Rectangular spectral collocation

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    Type
    Article
    Authors
    Driscoll, Tobin A.
    Hale, Nicholas
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2015-02-06
    Permanent link to this record
    http://hdl.handle.net/10754/599473
    
    Metadata
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    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.
    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)
    Journal
    IMA Journal of Numerical Analysis
    DOI
    10.1093/imanum/dru062
    ae974a485f413a2113503eed53cd6c53
    10.1093/imanum/dru062
    Scopus Count
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    Publications Acknowledging KAUST Support

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