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    Runge-Kutta methods with minimum storage implementations

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    Type
    Article
    Authors
    Ketcheson, David I. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Numerical Mathematics Group
    Date
    2010-03
    Permanent link to this record
    http://hdl.handle.net/10754/561436
    
    Metadata
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    Abstract
    Solution of partial differential equations by the method of lines requires the integration of large numbers of ordinary differential equations (ODEs). In such computations, storage requirements are typically one of the main considerations, especially if a high order ODE solver is required. We investigate Runge-Kutta methods that require only two storage locations per ODE. Existing methods of this type require additional memory if an error estimate or the ability to restart a step is required. We present a new, more general class of methods that provide error estimates and/or the ability to restart a step while still employing the minimum possible number of memory registers. Examples of such methods are found to have good properties. © 2009 Elsevier Inc. All rights reserved.
    Citation
    Ketcheson, D. I. (2010). Runge–Kutta methods with minimum storage implementations. Journal of Computational Physics, 229(5), 1763–1773. doi:10.1016/j.jcp.2009.11.006
    Sponsors
    The author thanks Randy LeVeque for the suggestion to consider embedded pairs. This work was funded by a US Dept. of Energy Computational Science Graduate Fellowship.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2009.11.006
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2009.11.006
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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