Search for efficient general linear methods for ordinary differential equations

摘要

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.