Codice | 56/2015 |
Titolo | Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions |
Data | 2015-11-02 |
Autore/i | Bonaventura, L.; Della Rocca, A. |
Link | Download full text | Pubblicato | L.Bonaventura,A.Della Rocca, Unconditional Strong Stability Preserving extensions of the TR-BDF2 method, Journal of Scientific Computing,Vol.70,pp.859-895,2017 |
Abstract | We analyze the one-step method TR-BDF2 from the point of view
of monotonicity, strong stability and positivity. All these properties
are strongly related and reviewed in the common framework of abso-
lute monotonicity. The radius of absolute monotonicity is computed
and it is shown that the parameter value which makes the method
L-stable is also the value which maximizes the radius of monotonicity.
Two hybrid variants of TR-BDF2 are proposed, that reduce the for-
mal order of accuracy and maximize the absolute monotonicity radius,
while keeping the native L-stability useful in stiff problems. Numeri-
cal experiments compare these different hybridization strategies with
other methods commonly used in the presence of stiff and mildly stiff
source terms. The results show that both strategies provide a good
compromise between accuracy and robustness at high CFL numbers,
without suffering from the limitations of alternative approaches al-
ready available in literature.
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