We consider advection-diffusion problems whose solution exhibits an oscillatory behaviour, such as the Boussinesq equation [1]. The semi-discretization in space of such equation gives rise to a system of ordinary differential equations, whose dimension depends on the number of spatial points. We present a general class of exponentially fitted two step peer methods for the numerical integration of ordinary differential equations having oscillatory solutions [2, 3]. Such methods are able to exploit a-priori known information about the qualitative behaviour of the solution in order to efficiently furnish an accurate solution. Moreover peer methods are very suitable for a parallel implementation, which may be necessary when the number of spatial points increases. The effectiveness of this problemoriented approach is shown through numerical tests on well-known problems. References [1] A. Cardone, R. D’Ambrosio, B. Paternoster (2017). Exponentially fitted IMEX methods for advectiondiffusion problems, J. Comput. Appl. Math (316), 100–108. [2] D. Conte, R. D’Ambrosio, M. Moccaldi, B. Paternoster (2018). Adapted explicit two-step peer methods, J. Numer. Math., in press. [3] D. Conte, L. Moradi, B. Paternoster (2017). Adapted implicit two-step peer methods, in preparation.

Exponentially fitted peer methods for advection diffusion problems

Dajana Conte;Leila Moradi;Beatrice Paternoster;
2019-01-01

Abstract

We consider advection-diffusion problems whose solution exhibits an oscillatory behaviour, such as the Boussinesq equation [1]. The semi-discretization in space of such equation gives rise to a system of ordinary differential equations, whose dimension depends on the number of spatial points. We present a general class of exponentially fitted two step peer methods for the numerical integration of ordinary differential equations having oscillatory solutions [2, 3]. Such methods are able to exploit a-priori known information about the qualitative behaviour of the solution in order to efficiently furnish an accurate solution. Moreover peer methods are very suitable for a parallel implementation, which may be necessary when the number of spatial points increases. The effectiveness of this problemoriented approach is shown through numerical tests on well-known problems. References [1] A. Cardone, R. D’Ambrosio, B. Paternoster (2017). Exponentially fitted IMEX methods for advectiondiffusion problems, J. Comput. Appl. Math (316), 100–108. [2] D. Conte, R. D’Ambrosio, M. Moccaldi, B. Paternoster (2018). Adapted explicit two-step peer methods, J. Numer. Math., in press. [3] D. Conte, L. Moradi, B. Paternoster (2017). Adapted implicit two-step peer methods, in preparation.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11386/4723807
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact