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