Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Fekete, Imre; Conde, Sidafa; Shadid, John N.

doi:10.1016/j.cam.2022.114325

Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Journal Article · 14 April 2022 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2022.114325· OSTI ID:1870469

^[1]; Conde, Sidafa ^[2]; Shadid, John N. ^[3]

Eötvös Loránd University (Hungary); MTA-ELTE Numerical Analysis and Large Networks Research Group (Hungary)
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States); Univ. of New Mexico, Albuquerque, NM (United States)

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2 ≤ p ≤ 4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1870469

Report Number(s):: SAND2022-3682J; 704754

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Vol. 412; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Embedded pairs
Hyperbolic problems
Runge–Kutta methods
Step-size control
Strong stability preserving methods
Variable step-size

Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

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