Optimal Runge--Kutta Stability Regions

Details Optimal Runge--Kutta Stability Regions Optimal Runge--Kutta Stability Regions

2012-01-14

arxiv.org/abs/1201.3035v2

Mathematics

Numerical Analysis

Scientific paper

The stable step size for numerical integration of an initial value problem depends on the stability region of the integrator and the spectrum of the problem it is applied to. We present a fast, accurate, and robust algorithm, based on convex optimization, to select an optimal linearly stable Runge-Kutta stability polynomial of any order and any number of stages, for any initial value problem in which the spectrum of the Jacobian is available. Optimized methods with increased number of stages can be used to enhance the efficiency of many method-of-lines PDE discretizations. Examples of optimal stability polynomials for a variety of problems are given.

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