TY - GEN A1 - Schlegel, Martin A1 - Marquardt, Wolfgang A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation N2 - In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach. T3 - ZIB-Report - 02-38 KW - sensitivity evaluation KW - differential-algebraic systems KW - extrapolation methods KW - dynamic optimization KW - optimal control Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7052 ER - TY - GEN A1 - Ehrig, Rainald A1 - Nowak, Ulrich T1 - Algorithmen- und Softwareoptimierung für die Satellitenbahn- und Schwerefeldmodellierung N2 - Dieser Report enthält die Ergebnisse der Untersuchungen, die gemäss dem Forschungs-- und Entwicklungsvertrag Gravity zwischen dem GeoForschungsZentrum Potsdam und dem Konrad--Zuse--Zentrum Berlin vorgenommen wurden. Die damit vereinbarte wissenschaftliche Kooperation hat die folgenden Ziele: \item{die am GFZ vorhandenen Algorithmen und Softwaremodule auf ihre Effizienz hisichtlich Nutzung der Rechnerresourcen zu untersuchen und Lösungen für einen schnelleren Datendurchsatz zu entwickeln und zu implementieren,} \item{Methoden zur Regularisierung und Lösung schlecht konditionierter Normalgleichungssysteme (für Schwerefeldkoeffizienten) kritisch zu untersuchen und eine mathematisch objektive Strategie der Regularisierung zu entwickeln, und} \item{insbesondere im Hinblick auf die Anforderungen bei GRACE, verschiedene Bahnintegrationsverfahren hinsichtlich ihrer numerischen Genauigkeit und Einsatzmöglichkeiten zu untersuchen.} T3 - ZIB-Report - 00-01 KW - geodesy KW - gravity field models KW - regularization KW - ill-posed systems KW - orbit integration Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5694 ER - TY - GEN A1 - Hohage, Thorsten A1 - Schmidt, Frank T1 - On the Numerical Solution of Nonlinear Schrödinger type equations in fiber optics N2 - The aim of this paper is to develop fast methods for the solution of nonlinear Schrödinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usually done by a Split Step method. Here we consider the extrapolation of Split Step methods with adaptive order and step size control. For more complicated nonlinearities, in particular stimulated Raman scattering, Split Step methods are less efficient since symmetry is either destroyed or requires much additional effort. In this case we use implicit Runge Kutta formulas of Gauß type. The key point for the efficient implementation of these methods is that the system of nonlinear algebraic equations can be solved without setting up the Jacobian. The proposed methods are compared to other methods, in particular exponential integrators, the method of Marcuse, and the method of Blow and Wood. T3 - ZIB-Report - 02-04 KW - nonlinear Schroedinger equation KW - split step methods KW - extrapolation KW - collocation methods Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6715 ER -