Resumen de Search for efficient general linear methods for ordinary differential equations

Maria Bras Amorós , Zdzislaw Jackiewicz

• 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.