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arXiv · 1207.2902

Strong stability preserving explicit Runge-Kutta methods of maximal effective order

Yiannis Hadjimichael·Colin B. Macdonald·David I. Ketcheson·James H. Verner
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Abstract

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge-Kutta methods. Relative to classical Runge-Kutta methods, methods with an effective order of accuracy are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods - like classical order five methods - require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge-Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice.

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Yiannis Hadjimichael, Colin B. Macdonald, David I. Ketcheson, James H. Verner. 2012-07-12. Strong stability preserving explicit Runge-Kutta methods of maximal effective order. https://doi.org/10.1137/120884201

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