Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters

summary:In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of suitable symbols enables the authors to generalize the Runge-Kutta formulas. The starting point for the construction of adaptive R. K. method was the consistent $s$-stage R. K. formula. Finally, the S-stability of the ARK method is investigated

Runge-Kutta-Nyström-type parallel block predictor-corrector methods

This paper describes the construction of block predictor-corrector methods based on Runge-Kutta-Nystrom correctors. Our approach is to apply the predictor-corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h; i = 1; : : : ; r. In this way, at each step, a whole block of approximations to the exact solution at off-step points is computed. In the next step, these approximations are used to obtain a high-order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off-step points can be computed in parallel, the sequential costs of these block predictor-corrector methods are comparable with those of a conventional predictor-corrector method. Furthermore, by using Runge-KuttaNystr om corrector methods, the computation of the approximation at each off-step point is also highly parallel. By a number of widely-used test problems, a class of the resulting block predictor-corrector methods is compared wi..

Kognitive Kontrolle in Krisensituationen: Arbeitslosigkeit bei Lehrern Interviewleitfaden Krisenbewaeltigung

IAB-92-870-60 AE 164 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLE3. FassungDEGerman

Kognitive Kontrolle in Krisensituationen: Arbeitslosigkeit bei Lehrern Arbeitsbericht (1.Zwischenbericht) Oktober 1979 bis Mai 1980

IAB-92-870-60 AE 163 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman