Regions of stability, equivalence theorems and the Courant-Friedrichs-Lewy condition

Springer Science and Business Media LLC - Tập 49 - Trang 319-329 - 1986
J. M. Sanz-Serna1, M. N. Spijker2
1Departmento de Ecuaciones Funcionales, Facultad, de Ciencias, Universidad de Valladolid, Valladolid, Spain
2Institute of Applied Mathematics and Computer Science, University of Leiden, Leiden, The Netherlands

Tóm tắt

The celebrated CFL condition for discretizations of hyperbolic PDEs is shown to be equivalent to some results of Jeltsch and Nevanlinna concerning regions of stability ofk-step,m-stage linear methods for the integration of ODEs. We characterize the methods for the numerical integration of the model equation,u t=u x which are weakly stable when the mesh-ratio takes the maximum value allowed by the CFL condition. We provide new equivalence theorems between stability and convergence, which improve on the classical results.

Tài liệu tham khảo

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