Regions of stability,equivalence theorems and the Courant-Friedrichs-Lewy condition |
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Authors: | J M Sanz-Serna M N Spijker |
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Institution: | (1) Departmento de Ecuaciones Funcionales, Facultad, de Ciencias, Universidad de Valladolid, Valladolid, Spain;(2) Institute of Applied Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, 2333 AL Leiden, The Netherlands |
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Abstract: | Summary 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. |
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Keywords: | AMS(MOS): 65M10 CR: G1 8 |
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