We describe the search for explicit general linear methods in Nordsieck form for which the stability function has only two nonzero roots. This search is based on state-of-the-art optimization software. Examples of methods found in this way are given for order p = 5, p = 6, and p = 7.
Cardone, A., Jackiewicz, Z., & Mittelmann, H. (2012). Optimization-based search for nordsieck methods of high order with quadratic stability polynomials. Mathematical Modelling and Analysis, 17(3), 293-308. https://doi.org/10.3846/13926292.2012.685497
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