General Linear Methods were introduced in order to encompass a large family of numerical methods for the solution of ODE-IVPs, ranging from LMF to RK formulae. In so doing, it is possible to obtain methods able to overcome typical drawbacks of the previous classes of methods. For example, stability limitations of LMF and order reduction for RK methods. Nevertheless, these goals are usually achieved at the price of a higher computational cost. Consequently, many efforts have been done in order to derive GLMs with particular features, to be exploited for their efficient implementation. In recent years, the derivation of GLMs from particular Boundary Value Methods (B VMs), namely the family of General- ized BDF (GBDF), has been proposed for the numerical solution of stiff ODE-IVPs. Here, this approach is further developed in order to derive GLMs combining good stability and accuracy properties with the possibility of efficiently solving the generated discrete problems via the blended implementation of the methods.
Blended General Linear Methods based on Generalized BDF / L.Brugnano; C.Magherini. - In: AIP CONFERENCE PROCEEDINGS. - ISSN 0094-243X. - STAMPA. - 1048:(2008), pp. 871-874. (Intervento presentato al convegno ICNAAM 2008 tenutosi a Kos (Greece) nel 16-20 settembre 2008) [10.1063/1.2991070].
Blended General Linear Methods based on Generalized BDF
BRUGNANO, LUIGI;
2008
Abstract
General Linear Methods were introduced in order to encompass a large family of numerical methods for the solution of ODE-IVPs, ranging from LMF to RK formulae. In so doing, it is possible to obtain methods able to overcome typical drawbacks of the previous classes of methods. For example, stability limitations of LMF and order reduction for RK methods. Nevertheless, these goals are usually achieved at the price of a higher computational cost. Consequently, many efforts have been done in order to derive GLMs with particular features, to be exploited for their efficient implementation. In recent years, the derivation of GLMs from particular Boundary Value Methods (B VMs), namely the family of General- ized BDF (GBDF), has been proposed for the numerical solution of stiff ODE-IVPs. Here, this approach is further developed in order to derive GLMs combining good stability and accuracy properties with the possibility of efficiently solving the generated discrete problems via the blended implementation of the methods.File | Dimensione | Formato | |
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