Differential-difference Equations/differential-differenzengleichungen: Applications And Numerical Problems/anwendungen Und Numerische Probleme (international Series Of Numerical Mathematics)

the following result: Using an integration method of order p tagether with polynomial interpolation of degree p -and constant stepsize h , where T is some multiple of h , leads to a pure interpolation error in each step for x ; : : : : x 0 + T . The integration error is zero. Therefore one should be cautions when dealing with stepsize control (see ARNDT [1 ]). This explains that the notion of local error in retarded problems cannot be taken over from the theory of ordinary differential equation without change. Instead, one has also to take into consideration the local error of the interpolation procedure. Front Matter....Pages 1-8 The Influence of Interpolation on the Global Error in Retarded Differential Equations....Pages 9-17 Maximum Principles for Periodic Solutions of Linear Delay Differential Equations....Pages 19-24 A Numerical Procedure to Compute Many Solutions of Diffusion-Reaction Systems....Pages 25-36 Anwachsende Schwingungen bei einigen Differenzengleichungen mit multiplikativem Verzögerungsglied....Pages 37-47 Einschließung periodischer Lösungen bei einer Klasse von Differenzen-Differentialgleichungen....Pages 49-54 Estimating the Global Error of Runge-Kutta Approximations for Ordinary Differential Equations....Pages 55-71 Characteristic Roots of Discretized Functional Differential Equations....Pages 73-89 Periodic, Aperiodic, and Stochastic Behavior of Differential-Difference Equations Modeling Biological and Economical Processes....Pages 91-108 Zellenfunktionen, Kohaerenz und Erweiterte Symmetrien bei Differenzenmethoden....Pages 109-118 Automatic Delay-Control in a Two-Phase Stefan Problem....Pages 119-135 Improved Absolute Stability of Predictor-Corrector Methods for Retarded Differential Equations....Pages 137-148 Approximation of the State of Infinite Delay and Volterra-Type Equations....Pages 149-168 Über die Existenz Positiver Periodischer Lösungen bei einem Allgemeinen Diffusionsmodell....Pages 169-175 Faktorisierung Linearer Differenzengleichungen mit Anwendungen auf Matrizen....Pages 177-187 Kardinale Splines, die Linearen Differenzengleichungen Genügen....Pages 189-196 Edited By L. Collatz, G. Meinardus, W. Wetterling.