A new approach to optimal B-convergence
A new approach is proposed for an investigation of the B-convergence [see \textit{R. Frank}, the author and \textit{C. W. Ueberhuber}, SIAM J. Numer. Anal. 18, 753-780 (1981; Zbl 0467.65032)] of the implicit midpoint rule, the implicit trapezoidal rule and the Lobatto IIIC scheme applied to a standard vector initial value problem \(y'=f(t,y)\), \(y(0)=y_ 0\). The approach is based on considering simultaneous perturbations on all steps of the numerical procedure rather than the propagation of a sequence of individual perturbations.
scientific article; zbMATH DE number 4016070
scientific article