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Computation of Optimal Monotonicity Preserving General Linear Methods

David I. Ketcheson
Mathematics of Computation
Vol. 78, No. 267 (Jul., 2009), pp. 1497-1513
Stable URL: http://www.jstor.org/stable/40234669
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Computation of Optimal Monotonicity Preserving General Linear Methods
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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.

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