Publications in Scientific Journals:
W. Auzinger, R. Frank, G. Kirlinger:
"An extension of B-convergence for Runge-Kutta methods";
Applied Numerical Mathematics,
The well-known concepts of B-stability and B-convergence for the analysis of one-step methods applied to stiff initial value problems are based on the notion of one-sided Lipschitz continuity. In a recent paper the authors have pointed out that the one-sided Lipschitz constant m must often be expected to be very large (positive and of the order of magnitude of the stiff eigenvalues) despite a (globally) well-conditioned behavior of the underlying problem. As a consequence, the existing B-theory suffers from considerable restrictions; e.g., not even linear systems with time dependent coefficients are satisfactorily covered.
The purpose of the present paper is to fill this gap; for implicit Runge-Kutta methods we extend the B-convergence theory such as to be valid for a class of non-autonomous weakly nonlinear stiff systems; reference to the (potentially large) one-sided Lipschitz constant is avoided. Unique solvability of the system of algebraic equations is shown, and global error bounds are derived.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.