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
Effect of Dielectric-Layer on the Stress Field of Micro Cantilever Beams at the Onset of Pull-In Instability
TL;DR: In this paper, the Modified Adomian Decomposition Method (MADM) is applied to obtain a semi-analytical solution for a distributed parameter model of the micro cantilever beam.
Journal ArticleDOI
Regularization of Equations of Motion of Celestial Bodies. 2. Correction of the KS-Coordinate System in Numerical Integration
TL;DR: In this paper, the problem of the optimal position of the radius vector and velocity at numerical integration in the KS-coordinate system is posed, and the solution of this problem, which reduces the number of calculations of the vector of perturbing accelerations, is given.
Journal ArticleDOI
Binary Interaction Approximation to N-Body Problems
Shun-ichi Oikawa,Hideo Funasaka +1 more
TL;DR: In this paper, the binary interaction approximation (BIA) was proposed to solve the N-body problem, which conserves total linear momenta in principle and other invariants such as the total angular momentum and total energy.
Journal ArticleDOI
A parallel implementation of the Stokesian Dynamics method applied to the simulation of colloidal suspensions
TL;DR: Through an efficient parallelization using the message passing system MPI, a strategy for the numerical simulation of polydisperse colloidal suspensions on supercomputers using distributed memory is presented, which allows the simulation of large colloidal systems to be simulated.
Proceedings ArticleDOI
Nonlinear dynamics of contact interaction of MEMS beam elements accounting the Euler-Bernoulli hypothesis in a temperature field
TL;DR: In this article, the authors proposed a methodology for determining the true chaos from the position of nonlinear dynamics for distributed mechanical systems in the form of a beam structure of two beams described by the kinematic first approximation hypothesis (Euler-Bernoulli).
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.