Computation of Optimal Monotonicity Preserving General Linear Methods
Type
ArticleAuthors
Ketcheson, David I.
KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
Office of the VP
Date
2009-04-27Online Publication Date
2009-04-27Print Publication Date
2009-09-01Permanent link to this record
http://hdl.handle.net/10754/138431
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Show full item recordAbstract
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/s0025-5718-09-02209-1Publisher
American Mathematical Society (AMS)Journal
Mathematics of Computationae974a485f413a2113503eed53cd6c53
10.1090/S0025-5718-09-02209-1