Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
TLDR
These new formulas are suitable for the numerical integration of heat transfer problems after discretisation of these problems in the space variables, since stability considerations, occurring in such problems, would eliminate the benefits of high-orderRunge-Kutta formulas.Abstract:
Es werden neue, expliziteRunge-Kutta-Formeln vierter und niedrigerer Ordnung mitgeteilt. Diese Formeln enthalten eine Schrittweiten-Kontrolle, die auf einer vollstandigen Erfassung des ersten Gliedes des lokalen Abbruchfehlers basiert. Die Formeln haben wesentlich kleinere Abbruchfehler als entsprechende Formeln anderer Autoren. Diese neuen Formeln eignen sich zur numerischen Integration von in den Raumvariablen diskretisierten Warmeleitungsproblemen, da die bei solchen Problemen auftretenden Stabilitatsverhaltnisse die zulassige Schrittweite vonRunge-Kutta-Formeln hoherer Ordnung beeintrachtigen wurden. Die Formeln werden auf ein Beispiel fur ein Warmeleitungsproblem angewandt.read more
Citations
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Journal ArticleDOI
Ensemble Kalman Filtering with a Divided State-Space Strategy for Coupled Data Assimilation Problems*
Xiaodong Luo,Ibrahim Hoteit +1 more
TL;DR: This work presents a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual subsystem, involving quantities from the subsystem itself and correlated quantities from other coupled subsystems.
Journal ArticleDOI
Towards Realistic Time-Resolved Simulations of Quantum Devices
Joseph Weston,Xavier Waintal +1 more
TL;DR: In this article, a flying qubit interferometer is simulated in the time domain, where the calculations are explicitly performed at the Fermi level and the presence of timedependent terms in the Hamiltonian makes the system inelastic so that it is necessary to explicitly enforce the Pauli principle in the simulations.
Journal ArticleDOI
Accuracy Considerations of Time-Splitting Methods for Models Using Two-Time-Level Schemes
TL;DR: A careful analysis of the basic method Wicker and Skamarock propose upon which they build their splitting scheme reveals that it is not strictly accurate to third order but is better thought of as a three-stage second-order method with superior characteristics of stability and accuracy.
Journal ArticleDOI
CASED: A simulation package designed for variable speed drives
TL;DR: CASED has shown itself to be a specialised and powerful tool in variable speed drive analysis and by choosing the correct DE solver the simulation time can be decreased by more than one hundred fold.
Journal ArticleDOI
Optimization of a pH-shift control strategy for producing monoclonal antibodies in Chinese hamster ovary cell cultures using a pH-dependent dynamic model.
TL;DR: This study proposed a new pH-dependent dynamic model represented by simultaneous differential equations including a minimum of six system component, depending on pH value that is suitable to optimize any pH-shift schedule for CHO cell lines used in mAb production projects.
References
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Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control
TL;DR: Runge-Kutta formulas of high order with stepsize control through leading truncation error term through leading parallelogram error term.
Journal ArticleDOI
Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
TL;DR: New explicit fifth- and seventh-orderRunge-Kutta formulas are derived that include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error.