We describe an algorithm, based on a new strategy recently proposed by Hewitt and Hill in the context of general linear methods, for the construction of algebraically stable two-step Runge-Kutta methods. Using this algorithm we obtained a complete characterization of algebraically stable methods with one and two stages.
Conte, D., D’Ambrosio, R., Jackiewicz, Z., & Paternoster, B. (2012). A practical approach for the derivation of algebraically stable two-step Runge-Kutta methods. Mathematical Modelling and Analysis, 17(1), 65-77. https://doi.org/10.3846/13926292.2012.644870
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