Results 201 to 210 of about 13,068 (272)

Multiplicative Runge–Kutta methods

Nonlinear Dynamics, 2007
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Dorota Aniszewska
exaly   +2 more sources

RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method

Expert Systems With Applications, 2021
Iman Ahmadianfar, Ali Asghar Heidari, Amir Gandomi   +2 more
exaly   +2 more sources

Total variation diminishing Runge-Kutta schemes

Mathematics of Computation, 1998
Sigal Gottlieb, Chi-Wang Shu
exaly   +2 more sources

Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms [PDF]

SIAM Journal on Numerical Analysis, 2019
We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be explicit and retain the accuracy and stability properties of the unmodified ...
David I Ketcheson
exaly   +2 more sources

RKformer: Runge-Kutta Transformer with Random-Connection Attention for Infrared Small Target Detection

ACM Multimedia, 2022
Infrared small target detection (IRSTD) refers to segmenting the small targets from infrared images, which is of great significance in practical applications.
Mingjin Zhang, Haichen Bai, Jing Zhang, Rui Zhang, Chaoyue Wang, Jie Guo, Xinbo Gao   +6 more
semanticscholar   +1 more source

A family of embedded Runge-Kutta formulae

Journal of Computational and Applied Mathematics, 1980
A family of embedded Runge-Kutta formulae RK5 (4) are derived. From these are presented formulae which have (a) ‘small’ principal truncation terms in the fifth order and (b) extended regions of absolute stability.
J. Dormand, P. Prince
exaly   +2 more sources

Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation

, 2021
Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn equation has been an open problem in recent years. This work provides a positive answer by designing and analyzing a class of up to fourth order maximum principle ...
Hong Zhang, Jingye Yan, Xu Qian, Songhe Song   +3 more
semanticscholar   +1 more source

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations

Journal of Computational Physics, 2020
A unified framework of invariant-conserving explicit Runge-Kutta schemes for the nonlinear Hamiltonian ODEs and PDEs are proposed by utilizing the invariant energy quadratization technique.
Hong Zhang, Xu Qian, Jingye Yan, Songhe Song   +3 more
semanticscholar   +1 more source

Error Estimate of the Fourth-Order Runge-Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis, 2020
In this paper we consider the Runge--Kutta discontinuous Galerkin (RKDG) method to solve linear constant-coefficient hyperbolic equations, where the fourth-order explicit Runge--Kutta time-marching...
Yuan Xu, Chi-Wang Shu, Qiang Zhang
semanticscholar   +1 more source

Higher-order additive Runge–Kutta schemes for ordinary differential equations

Applied Numerical Mathematics, 2019
Two new implicit–explicit, additive Runge–Kutta ( ARK 2 ) methods are given with fourth- and fifth-order formal accuracies, respectively. Both combine explicit Runge–Kutta (ERK) methods with explicit, singly-diagonally implicit Runge–Kutta (ESDIRK ...
C. Kennedy, M. Carpenter
semanticscholar   +1 more source