Search for efficient general linear methods for ordinary differential equations

Authors:
M. Bra;Z. Jackiewicz
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 20
Cited 0

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
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Abstract

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.