RUNGE-KUTTA_METHODS

作品数：63被引量：92H指数：4
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相关作者：刘梅林刘少斌王志勇李寿佛甘四清更多>>
相关机构：华东师范大学南京航空航天大学哈尔滨工业大学(威海)电子科技大学更多>>
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A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems被引量：1
《Communications in Computational Physics》2023年第2期477-510,共34页Weiwen Wang Chuanju Xu 
NSFC grant 11971408.
Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a nov...
关键词：Thermal phase change problem gradient flows unconditional energy stability auxiliary variable Runge-Kutta methods phase field 
On Energy Stable Runge-Kutta Methods for the Water Wave Equation and its Simplified Non-Local Hyperbolic Model
《Communications in Computational Physics》2022年第6期222-258,共37页Lei Li Jian-Guo Liu Zibu Liu Yi Yang Zhennan Zhou 
L.Li was supported by National Natural Science Foundation of China(Grant No.31571071);Shanghai Sailing Program 19YF1421300;J.-G.Liu was supported in part by DMS-2106988;Z.Zhou was supported by the National Key R&D Program of China,Project Number 2021YFA001200;the NSFC,grant number 12171013.
Although interest in numerical approximations of the water wave equationgrows in recent years, the lack of rigorous analysis of its time discretization inhibits thedesign of more efficient algorithms. In practice of w...
关键词：Runge-Kutta methods NON-LOCALITY HYPERBOLICITY 
On Dissipation and Dispersion Errors Optimization,A-Stability and SSP Properties
《Communications in Computational Physics》2018年第6期268-285,共18页Arman Rokhzadi Abdolmajid Mohammadian 
The authors wish to acknowledge financial support from NSERC。
In a recent paper(Du and Ekaterinaris,2016)optimization of dissipation and dispersion errors was investigated.A Diagonally Implicit Runge-Kutta(DIRK)scheme was developed by using the relative stability concept,i.e.the...
关键词：Diagonally Implicit Runge-Kutta methods dissipation and dispersion OPTIMIZATION numerical stability steady state 
Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems被引量：2
《Communications in Computational Physics》2017年第1期237-270,共34页Peng Wang Jialin Hong Dongsheng Xu 
This work was supported by NSFC(91130003);The first authors is also supported by NSFC(11101184,11271151);the Science Foundation for Young Scientists of Jilin Province(20130522101JH);The second and third authors are also supported by NSFC(11021101,11290142).The authors would like to thank anonymous reviewers for careful reading and invaluable suggestions,which greatly improved the presentation of the paper.
We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respe...
关键词：Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition 
Exponential Runge-Kutta Methods for the Multispecies Boltzmann Equation被引量：1
《Communications in Computational Physics》2014年第4期996-1011,共16页Qin Li Xu Yang 
supported by the NSF grant DMS-1114546 and NSF Research Network in Mathematical Sciences“KI-Net:Kinetic description of emerging challenges in multiscale problems of natural sciences”;X.Y.was partially supported by the startup funding of University of California,Santa Barbara。
This paper generalizes the exponential Runge-Kutta asymptotic preserving(AP)method developed in[G.Dimarco and L.Pareschi,SIAM Numer.Anal.,49(2011),pp.2057–2077]to compute the multi-species Boltzmann equation.Compared...
关键词：Multispecies Boltzmann equation exponential Runge-Kutta method hydrodynamic limit asymptotic preserving property positivity preserving 
Explicit Multi-Symplectic Methods for Hamiltonian Wave Equations
《Communications in Computational Physics》2007年第4期662-683,共22页Jialin Hong Shanshan Jiang Chun Li Hongyu Liu 
supported by the Director Innovation Foundation of ICMSEC and AMSS,the Foundation of CAS,the NNSFC(No.19971089 and No.10371128);the National Basic Research Program of China under the Grant 2005CB321701.
In this paper,based on the multi-symplecticity of concatenating symplectic Runge-Kutta-Nystrom(SRKN)methods and symplectic Runge-Kutta-type methods for numerically solving Hamiltonian PDEs,explicit multi-symplectic sc...
关键词：Hamiltonian wave equations multi-symplectic integration symplectic Runge-Kutta methods symplectic Runge-Kutta-Nystrom methods. 
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