Search for efficient general linear methods for ordinary differential equations

• Autores: Maria Bras Amorós , Zdzislaw Jackiewicz
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 262, Nº 1, 2014, págs. 180-192
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.07.032
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• Resumen

  • We analyze implicit general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s or q = s + 1. These methods might eventually lead to more efficient formulas than the class of DIMSIMs and the class of general linear methods with inherent Runge�Kutta stability. We analyze also error propagation and estimation of local discretization errors. Examples of such methods which are A- and L-stable are derived up to the stage order q = 3 or q = 4 and order p = 4.