Summary
Stability regions of explicit “linear” time discretization methods for solving initial value problems are treated. If an integration method needsm function evaluations per time step, then we scale the stability region by dividing bym. We show that the scaled stability region of a method, satisfying some reasonable conditions, cannot be properly contained in the scaled stability region of another method. Bounds for the size of the stability regions for three different purposes are then given: for “general” nonlinear ordinary differential systems, for systems obtained from parabolic problems and for systems obtained from hyperbolic problems. We also show how these bounds can be approached by high order methods.
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This research has been supported by the Swiss National Foundation, grant No. 82-524.077
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Jeltsch, R., Nevanlinna, O. Stability of explicit time discretizations for solving initial value problems. Numer. Math. 37, 61–91 (1981). https://doi.org/10.1007/BF01396187
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DOI: https://doi.org/10.1007/BF01396187