Strong-Stability-Preserving Hermite—Birkhoff Time-Discretizations of Order 4 to 12
Abstract
Optimal strong-stability-preserving Hermite—Birkhoff (SSP HB) methods, HBksp, of order p = 4,5,...,12 have been constructed by combining k-step methods of order p = 1,2,...,9 and s-stage Runge—Kutta (RK) methods of order 4, with s = 4,5,...,10. These methods are well suited for solving discretized hyperbolic PDEs by the methods of lines. The Shu—Osher representation of RK methods is extended to the above SSP HB methods. The HBksp having the largest effective SSP coefficient have been found numerically among the HB methods of order p on hand. Several high-order SSP HB methods are compared with SSP RK methods of order 4.
- Publication:
-
Advances in Mathematical and Computational Methods: Addressing Modern Challenges of Science, Technology, and Society
- Pub Date:
- November 2011
- DOI:
- 10.1063/1.3663512
- Bibcode:
- 2011AIPC.1368..275N
- Keywords:
-
- number theory;
- finite element analysis;
- finite difference methods;
- integration;
- 02.10.De;
- 02.70.Dh;
- 02.70.Bf;
- 02.30.Cj;
- Algebraic structures and number theory;
- Finite-element and Galerkin methods;
- Finite-difference methods;
- Measure and integration