Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions

56/2015

Monotonicity, positivity and strong stability of the TR-BDF2 method and of its SSP extensions

Monday 2nd November 2015

Bonaventura, L.; Della Rocca, A.

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.

This report, or a modified version of it, has been also submitted to, or published on
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