Results 41 to 50 of about 32,630,588 (240)

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

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

DIRK Schemes with High Weak Stage Order

, 2020
Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems.
A Ditkowski, A Ostermann, A Prothero, G Wanner, JC Butcher, JG Verwer, JM Sanz-Serna, K Burrage, MH Carpenter, ML Minion   +9 more
core   +1 more source

Exponential Runge-Kutta methods for stiff kinetic equations [PDF]

, 2010
We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK ...
Dia B. O., Giacomo Dimarco, Lorenzo Pareschi, Pareschi L., Villani C.   +4 more
core   +3 more sources

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

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

Transient Terahertz Oscillations During Photoinduced Polarization Topology Reconfiguration in Ferroelectric Superlattices

Advanced Science, EarlyView.
Terahertz resonances in crystalline heterostructures could close a spectral gap between conventional electronics and photonics while opening new windows on non‐equilibrium lattice dynamics. Femtosecond optical screening of the depolarization field in epitaxial PbTiO3/SrTiO3 superlattices launches a collective polar mode that oscillates near 1 THz and ...
Deepankar Sri Gyan, Hyeon Jun Lee, Xiangwei Guo, Youngjun Ahn, Samuel D. Marks, Mohammed H. Yusuf, Matthew Dawber, James M. Glownia, Diling Zhu, Takahiro Sato, Sanghoon Song, Haidan Wen, Jia‐Mian Hu, Paul G. Evans   +13 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

Efficiency of different numerical methods for solving Redfield equations [PDF]

, 2000
The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as
Kleinekathoefer, Ulrich, Kondov, Ivan, Schreiber, Michael   +2 more
core   +2 more sources

Superradiance and Broadband Emission Driving Fast Electron Dephasing in Open Quantum Systems

Advanced Science, EarlyView.
We uncover the physical origin of ultrafast electron dephasing in solid‐state high‐harmonic generation by simulating the Lindblad equation for the dissipative Hubbard model. Coexistence of Dicke superradiance and broadband emission is revealed, whose destructive interference shortens the effective scattering time and provides a unified picture of ...
Gimin Bae, Youngjae Kim, Jae Dong Lee
wiley   +1 more source