AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland; Jagiellonian University, Faculty of Mathematics and Computer Science ul. prof. S. Lojasiewicza 6, 30-348 Krakow, Poland
School of Mathematical & Statistical Sciences, Arizona State University Tempe, Arizona 85287; AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland
We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.
Bras, M., & Jackiewicz, Z. (2014). Efficient General Linear Methods of High Order with Inherent Quadratic Stability. Mathematical Modelling and Analysis, 19(4), 450-468. https://doi.org/10.3846/13926292.2014.955893
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