A study of B-convergence of linearly implicit Runge-Kutta methods (Q1114354)

This paper analyses the B-convergence properties of linearly implicit Runge-Kutta methods when applied to stiff semi-linear problems. Sufficient conditions for a method to be B-consistent with a certain order are derived. A generalization of \textit{J. F. B. M. Kraaijevanger}'s technique [BIT 25, 652-666 (1985; Zbl 0584.65048)] for establishing the B-convergence of the implicit midpoint rule is used to demonstrate that for a certain singularly perturbed subclass of semi-linear problems the B-convergence order can be one more than the B-consistent order. Some numerical examples illustrate these points.