We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute 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. In order to achieve unconditional monotonicity, hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy, while keeping the native L-stability property, which is useful for the application to stiff problems. Numerical experiments compare these different hybridization strategies to other methods used in stiff and mildly stiff problems. The results show that the proposed strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in literature.

Unconditionally Strong Stability Preserving Extensions of the TR-BDF2 Method

BONAVENTURA, LUCA;
2017-01-01

Abstract

We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute 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. In order to achieve unconditional monotonicity, hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy, while keeping the native L-stability property, which is useful for the application to stiff problems. Numerical experiments compare these different hybridization strategies to other methods used in stiff and mildly stiff problems. The results show that the proposed strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in literature.
2017
Absolute monotonicity; Positivity preservation; Runge–Kutta; SSP; TR-BDF2; TVD; Software; Theoretical Computer Science; Engineering (all); Computational Theory and Mathematics
File in questo prodotto:
File Dimensione Formato  
11311-1008157_Bonaventura.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 2.9 MB
Formato Adobe PDF
2.9 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1008157
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 22
social impact