One step integration methods with maximum stability regions (Q794143)

For all \(K\in {\mathbb{N}}\) stability polynomials M(z) of one-step K-stage schemes are given which have the maximal stability interval K-1 on the imaginary axis. Moreover it is shown that for these polynomials one has \(M(i(K-1))=\exp(i(K-1)\pi /2).\) The schemes are of oder one or two only. For stability polynomials of order 3 or 4 and large stability intervals on the imaginary axis see the following review.