Abstract (may include machine translation)
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.
Original language | English |
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Article number | 114325 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 412 |
DOIs | |
State | Published - 1 Oct 2022 |
Externally published | Yes |
Keywords
- Embedded pairs
- Hyperbolic problems
- Runge–Kutta methods
- Step-size control
- Strong stability preserving methods
- Variable step-size