The exponential fitting technique uses information on the expected behaviour of the solution of ordinary and partial differential equations to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when applied to problems with oscillatory solutions. In these cases, they perform better than standard methods, particularly in the large time-step regime. In this paper we consider exponentially fitted Runge-Kutta methods and we give characterizations of those that preserve local conservation laws of linear and quadratic quantities. As a benchmark for the general theory we apply the symplectic midpoint and its exponentially fitted version to approximate breather wave solutions of partial differential equations arising as models in several fields, such as fluid dynamics and quantum physics. Numerical tests show that the exponentially fitted method performs better and its solution exactly satisfy discrete conservation laws of mass (or charge) and momentum.

Exponentially fitted methods that preserve conservation laws

Conte, Dajana;Frasca-Caccia, Gianluca
2022-01-01

Abstract

The exponential fitting technique uses information on the expected behaviour of the solution of ordinary and partial differential equations to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when applied to problems with oscillatory solutions. In these cases, they perform better than standard methods, particularly in the large time-step regime. In this paper we consider exponentially fitted Runge-Kutta methods and we give characterizations of those that preserve local conservation laws of linear and quadratic quantities. As a benchmark for the general theory we apply the symplectic midpoint and its exponentially fitted version to approximate breather wave solutions of partial differential equations arising as models in several fields, such as fluid dynamics and quantum physics. Numerical tests show that the exponentially fitted method performs better and its solution exactly satisfy discrete conservation laws of mass (or charge) and momentum.
2022
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/11386/4778591
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact