Results 31 to 40 of about 11,954,701 (266)

Explicit two-step Runge-Kutta methods [PDF]

, 1995
summary:The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described.
Zennaro, Marino, Renaut, Rosemary Anne, Jackiewicz, Zdzislaw   +2 more
core   +1 more source

A class of implicit-explicit two-step Runge-Kutta methods [PDF]

, 2012
This work develops implicit-explicit time integrators based on two-step Runge-Kutta methods. The class of schemes of interest is characterized by linear invariant preservation and high stage orders.
Zharovski, Evgeniy, Sandu, Adrian
core   +1 more source

Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2016
In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
doaj   +1 more source

Order conditions of stochastic Runge-Kutta methods by B-series [PDF]

, 2000
In this paper, general order conditions and a global convergence proof are given for stochastic Runge-Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied
Burrage, Pamela, Burrage, P. M., Burrage, Kevin, Burrage, K.   +3 more
core   +1 more source

Efficient explicit time integration for the simulation of acoustic and electromagnetic waves [PDF]

, 2015
The efficient and accurate numerical simulation of time-dependent wave phenomena is of fundamental importance in acoustic, electromagnetic or seismic wave propagation.
Mehlin, Michaela
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

On modified Runge–Kutta trees and methods

Computers & Mathematics with Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Charalampos Tsitouras, Ioannis Th. Famelis, T. E. Simos   +2 more
openaire   +2 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

Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models [PDF]

Geoscientific Model Development, 2018
The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves.
D. J. Gardner, J. E. Guerra, F. P. Hamon, D. R. Reynolds, P. A. Ullrich, C. S. Woodward   +5 more
doaj   +1 more source