Journal ArticleDOI
Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
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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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DissertationDOI
Simulation and optimization of logical and kinetic biochemical models
TL;DR: An algorithm for the simulation of models given in the Systems Biology Markup Language (SBML) is described and applied in a large study investigating the influence of experimental noise on the estimation of kinetic parameters for three published drugs.
Journal ArticleDOI
Expressions for the fractional modification in different monocyclic enzyme cascade systems: analysis of their validity tested by numerical integration.
Ramón Varón,Edelmira Valero,Milagros Molina-Alarcón,F. García-Cánovas,Francisco Garcia-Molina,M. E. Fuentes,Manuela García-Moreno +6 more
TL;DR: From this general expression, under a minimal set of assumptions, a general expression for the steady-state fractional modification of an interconvertible protein involved in four different schemes of monocyclic enzyme cascade systems is derived.
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Quantum Thermodynamics: Non-equilibrium 3D Description of an Unbounded System at an Atomistic Level
TL;DR: In this article, the authors extend the work reported in previous papers of modeling the storage of hydrogen in an isolated system, by extending the modeling to 3D, and show in detail the trajectory of the state of the system as the hydrogen molecules, which are initially arranged to be far from the carbon nanotube, spread out in the system and eventually become more concentrated near the carbon atoms which make up the carbon atom.
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A Multi-Interval Homotopy Analysis Method Using Multi-Objective Optimization for Analytically Analyzing Chaotic Dynamics in Memristive Circuit
TL;DR: A novel analytical method for analyzing the chaotic trajectories of memristive circuit is proposed, characterized by higher approximation accuracy and computational performance among the homotopy-based analytical methods, due to the optimized convergence control parameters in subintervals.
Journal ArticleDOI
Efficient variable stiffness methods for cooling of hot-rolled steel sections
TL;DR: In this article, an industrial finite element package for the simulation of alternative cooling strategies for hot-rolled steel sections has been enhanced by the incorporation of a variable stiffness second-order timeintegration scheme, based on a specially developed family of extended-stability explicit Runge-Kutta methods, and an L-stable semi-implicit formula.
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.