Kraaijevanger–MacDonald–Gottlieb conjecture on the radius of absolute monotonicity

Let A,bA,b denote the coefficients of an implicit Runge–Kutta method of order p2p\ge 2 with s1s\ge 1 stages. Its radius of absolute monotonicity is denoted by R(A,b)R(A,b).

Kraaijevanger–MacDonald–Gottlieb conjecture. For every such method,

R(A,b)2s.R(A,b)\le 2s.

This conjecture concerns the sharp upper bound for the strong-stability-preserving coefficient of implicit Runge–Kutta methods. The source states that it had previously been proved only for s=1s=1 or s=2s=2; its status here is recorded as resolved.

Sources & referencesView supporting material

Primary source

Lajos Loczi and David I. Ketcheson, “Rational functions with maximal radius of absolute monotonicity”, arXiv:1303.6651 (2013).

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