Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776676 | Applied Numerical Mathematics | 2017 | 40 Pages |
Abstract
The order reduction phenomenon for general linear methods (GLMs) for stiff differential equations is investigated. It turns out that, similarly as for standard Runge-Kutta methods, the effective order of convergence for a large class of GLMs applied to stiff differential systems, is equal to the stage order of the method. In particular, it is demonstrated that the global error âe[n]â of GLMs of order p and stage order q applied to the Prothero-Robinson test problem yâ²(t)=λ(y(t)âÏ(t))+Ïâ²(t), tâ[t0,T], y(t0)=Ï(t0), is O(hq)+O(hp) as hâ0 and hλâââ. Moreover, for GLMs with Runge-Kutta stability which are A(0)-stable and for which the stability function R(z) of the underlying Runge-Kutta methods, (i.e., the corresponding RK methods which have the same absolute stability properties as the GLMs), is such that R(â)â 1, the global error satisfies âe[n]â=O(hq+1)+O(hp) as hâ0 and hλâââ. These results are confirmed by numerical experiments.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
MichaÅ BraÅ, Angelamaria Cardone, ZdzisÅaw Jackiewicz, Bruno Welfert,