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

Journal Article · · Journal of Computational and Applied Mathematics
ORCiD logo [1];  [2];  [3]
  1. Eötvös Loránd University (Hungary); MTA-ELTE Numerical Analysis and Large Networks Research Group (Hungary)
  2. Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
  3. 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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
Report Number(s):
SAND2022-3682J; 704754
Journal Information:
Journal of Computational and Applied Mathematics, Vol. 412; ISSN 0377-0427
ElsevierCopyright Statement
Country of Publication:
United States

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