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
More filters
Journal ArticleDOI
Massively parallel computation of atmospheric neutrino oscillations on CUDA-enabled accelerators
TL;DR: Two scalable multi-GPU extensions of common neutrino oscillation frameworks are introduced – namely Prob3++ and ν SQuIDS –allowing for the acceleration of oscillation dynamics computation by one to three orders ofmagnitude while preserving numerical accuracy.
Journal ArticleDOI
Rational Approximations for Heat Radiation and Troesch’s Equations
TL;DR: In this paper, a new tool for the solution of nonlinear differential equations is presented, named rational homotopy perturbation method (RHPM), which delivers a high precision representation of the non-linear differential equation using a few linear algebraic terms.
Journal ArticleDOI
An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology
TL;DR: In this article, the authors designed and developed an effective numerical calculation method to improve the time stiff problem, which consisted of ahead, backward, and cumulative algorithms, and reduced the number of numerical calculations required for multi-time-scale models with the time-stiff problem.
Journal ArticleDOI
Algebraic Analysis Approach for Multibody Problems
Shun-ichi Oikawa,Hideo Funasaka +1 more
TL;DR: For a 108-body problem, which corresponds to full three-dimensional Coulomb interactions within the Debye sphere in a fusion plasma, the ALG approximation is 263 times as fast as the 6-stage 5th order Runge-Kutta-Fehlberg method with an absolute error tolerance of 10−16.
Journal ArticleDOI
Benchmarking numerical methods for lattice equations with the Toda lattice
Deniz Bilman,Thomas Trogdon +1 more
TL;DR: In this paper, the performance of well-known numerical time-stepping methods that are widely used to compute solutions of the doubly-infinite Fermi-Pasta-Ulam-Tsingou (FPUT) lattice equations is compared.
References
More filters
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.