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    Computation of Optimal Monotonicity Preserving General Linear Methods

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    Type
    Article
    Authors
    Ketcheson, David I. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Mathematics Group
    Office of the VP
    Date
    2009-04-27
    Online Publication Date
    2009-04-27
    Print Publication Date
    2009-09-01
    Permanent link to this record
    http://hdl.handle.net/10754/138431
    
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    Abstract
    Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.
    Citation
    Ketcheson, D. I. (2009). Computation of optimal monotonicity preserving general linear methods. Mathematics of Computation, 78(267), 1497–1513. doi:10.1090/s0025-5718-09-02209-1
    Publisher
    American Mathematical Society (AMS)
    Journal
    Mathematics of Computation
    DOI
    10.1090/S0025-5718-09-02209-1
    ae974a485f413a2113503eed53cd6c53
    10.1090/S0025-5718-09-02209-1
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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