Results 41 to 50 of about 32,424,344 (291)

Spatially partitioned embedded Runge-Kutta Methods [PDF]

, 2013
We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain.
Ketcheson, D. I., Macdonald, C. B., Ruuth, S. J.   +2 more
core   +2 more sources

Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations [PDF]

, 2007
Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and ...
Botchev, M.A., Sármány, D., Vegt, J.J.W. van der   +2 more
core   +2 more sources

Track parameter propagation through the application of a new adaptive Runge-Kutta-Nystrom method in the ATLAS experiment [PDF]

, 2008
In this paper we study several fixed step and adaptive Runge-Kutta methods suitable for transporting track parameters through an inhomogeneous magnetic field.
Bugge, L, Gavrilenko, I, Lund, E, Strandlie, A   +3 more
core   +1 more source

Composite group of explicit Runge-Kutta methods [PDF]

, 2016
In this paper,the composite groups of Runge-Kutta (RK) method are proposed. The composite group of RK method of third and second order, RK3(2) and fourth and third order RK4(3) base on classical Runge-Kutta method are derived.
Abd Hamid, Fatin Nadiah, Ismail, Fudziah, Rabiei, Faranak   +2 more
core   +1 more source

Dissipativity of Runge-Kutta methods for a class of nonlinear functional-integro-differential equations

Advances in Difference Equations, 2017
This paper is concerned with the dissipativity of Runge-Kutta methods for a class of nonlinear functional-integro-differential equations (FIDEs). The dissipativity results of Runge-Kutta methods for the FIDEs are given.
Qing Liao, Liping Wen
doaj   +1 more source

A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes

The Astrophysical Journal, 2022
In recent publications, the construction of explicit symplectic integrators for Schwarzschild- and Kerr-type spacetimes is based on splitting and composition methods for numerical integrations of Hamiltonians or time-transformed Hamiltonians associated ...
Naying Zhou, Hongxing Zhang, Wenfang Liu, Xin Wu   +3 more
doaj   +1 more source

Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses

Mathematics
In this paper, we study the asymptotical stability of the exact solutions of nonlinear impulsive differential equations with the Lipschitz continuous function f(t,x) for the dynamic system and for the impulsive term Lipschitz continuous delayed functions
Gui-Lai Zhang, Zhi-Yong Zhu, Yu-Chen Wang, Chao Liu   +3 more
doaj   +1 more source

Clean Up Behind You ‐ Novel Patterning Approach for Solid Immersion Lenses

Advanced Functional Materials, EarlyView.
A focused ion beam (FIB) milling strategy enables rapid fabrication of solid immersion lenses (SILs) with smooth, debris‐free surfaces eliminating the need for post‐processing. The optimized pattern improves efficiency and surface quality. SILs containing NV centers are also investigated, confirming the technique's suitability for quantum and photonic ...
Aleksei Tsarapkin, Stefan Facsko, Wentao Zhang, Anna Mogilatenko, Kilian Unterguggenberger, Bailiang Li, Cem Güney Torun, Gerhard Hobler, Tommaso Pregnolato, Tim Schröder, Katja Höflich   +10 more
wiley   +1 more source

Derivation of Three-Derivative Two-Step Runge–Kutta Methods

Mathematics
In this paper, we develop explicit three-derivative two-step Runge–Kutta (ThDTSRK) schemes, and propose a simpler general form of the order accuracy conditions (p≤7) by Albrecht’s approach, compared to the order conditions in terms of rooted trees.
Xueyu Qin, Jian Yu, Chao Yan
doaj   +1 more source

Continuous-Stage Runge–Kutta Approximation to Differential Problems

Axioms, 2022
In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs).
Pierluigi Amodio, Luigi Brugnano, Felice Iavernaro   +2 more
doaj   +1 more source