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
Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.
TL;DR: The orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis–Menten kinetics.
Journal ArticleDOI
Adaptive Brownian Dynamics.
TL;DR: In this article, a framework for performant Brownian Dynamics (BD) many-body simulations with adaptive timestepping is presented, which employs an embedded Heun-Euler integrator for the propagation of the overdamped coupled Langevin equations of motion.
Journal ArticleDOI
Time-optimal control of an inverted pendulum in the feedback form
S. A. Reshmin,F. L. Chernous’ko +1 more
TL;DR: In this article, a time-optimal feedback control is synthesized that steers a nonlinear pendulum to the top unstable equilibrium position, based on the maximum principle and involves an analytical investigation in combination with numerical computations.
Journal ArticleDOI
Parameter range reduction for ODE models using cumulative backward differentiation formulas
TL;DR: This work introduces the class of cumulative backward differentiation formulas (CBDFs) and shows that they inherit the accuracy and stability properties of their generating backward differentiation formula (BDFs), and results in reductions of the parameter ranges that are better than can be obtained simply using BDFs.
Journal ArticleDOI
Helical structure of ventricular anatomy by diffusion tensor cardiac MR tractography.
TL;DR: There is a lack of consensus about the distribution of the myocardial fibers and their spatial arrangement in the left and right ventricles, but there is an understanding of the role of these fibers in contractility and relaxation.
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.