Grid strategy and high accuracy via defect corrections for the Kreiss- method for stiff boundary value problems (Q1820564)

Based on the Kreiss-method for stiff boundary value problems [cf. \textit{B. Kreiss}, \textit{H.-O. Kreiss}, SIAM J. Numer. Anal. 18, 262-276 (1981; Zbl 0457.65064); \textit{H.-O. Kreiss}, \textit{N. K. Nicols}, \textit{D. L. Brown}, ibid. 23, 325-368 (1986; Zbl 0608.65049)] defect corrections are applied. The first step in the defect correction is used to iteratively build up an appropriate grid for the stiff boundary value problem. Having found this grid, the full defect correction machinery is used to get high accuracy results. The same time, which has to be spent for the original Kreiss-approach to define the grid, is enough in our approach to define the grid and, in addition, to compute high accuracy approximations. The accuracy is better by many powers of ten than the original Kreiss- approach.