Optimal explicit strong stability preserving Runge--Kutta methods with high linear order and optimal nonlinear order
linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These meth...
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| Published in: | Mathematics of computation Vol. 84; no. 296; pp. 2743 - 2761 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
American Mathematical Society
01-11-2015
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| Online Access: | Get full text |
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| Summary: | linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.]]> |
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| ISSN: | 0025-5718 1088-6842 |
| DOI: | 10.1090/mcom/2966 |