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RUNGE-KUTTA_METHODS: 作品数：63被引量：92H指数：4; 导出分析报告; 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>>; 相关期刊：《Journal of Computational Mathematics》《Advances in Aerodynamics》《Transactions of Nanjing University of Aeronautics and Astronautics》《Applied Mathematics and Mechanics(English Edition)》更多>>; 相关基金：国家自然科学基金中国博士后科学基金国家重点基础研究发展计划国家高技术研究发展计划更多>>

Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay: 《Acta Mathematicae Applicatae Sinica》2025年第2期400-413,共14页Cheng-jian ZHANG Yang WANG Hao HAN; supported by the National Natural Science Foundation of China(Grant No.12471379).; This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs)with time-variable delay.For solving this kind of delay BVPs,by combining Runge-Kutta methods with Lagrange interpolatio...; 关键词：delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

Stability Analysis and Performance Evaluation of Additive Mixed-Precision Runge-Kutta Methods: 《Communications on Applied Mathematics and Computation》2024年第1期705-738,共34页Ben Burnett Sigal Gottlieb Zachary J.Grant; supported by ONR UMass Dartmouth Marine and UnderSea Technology(MUST)grant N00014-20-1-2849 under the project S31320000049160;by DOE grant DE-SC0023164 sub-award RC114586-UMD;by AFOSR grants FA9550-18-1-0383 and FA9550-23-1-0037;supported by Michigan State University,by AFOSR grants FA9550-19-1-0281 and FA9550-18-1-0383;by DOE grant DE-SC0023164.; Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implic...; 关键词：Mixed precision Runge-Kutta methods Additive methods ACCURACY

ON THE EXPLICIT TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS被引量：1: 《Journal of Computational Mathematics》2023年第2期305-324,共20页Yuhuan Yuan Huazhong Tang; partially supported by the Special Project on Highperformance Computing under the National Key R&D Program(No.2020YFA0712002);the National Natural Science Foundation of China(No.12126302,12171227).; This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,...; 关键词：Multistage multiderivative methods Runge-Kutta methods Absolute stability region Interval of absolute stability

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

Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics: 《Communications on Applied Mathematics and Computation》2022年第4期1191-1228,共38页Hendrik Ranocha Lisandro Dalcin Matteo Parsani David I.Ketcheson; Open Access funding enabled and organized by Projekt DEAL.; We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusi...; 关键词：Explicit Runge-Kutta methods Step size control Compressible Euler equations Compressible Navier-Stokes equations hp-adaptive spatial discretizations

A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation: 《Numerical Mathematics(Theory,Methods and Applications)》2022年第3期768-792,共25页Yue Chen Yuezheng Gong Qi Hong Chunwu Wang; supported by the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202002);the Natural Science Foundation of Jiangsu Province(Grant No.BK20180413);the National Natural Science Foundation of China(Grant Nos.11801269,12071216);supported by Science Challenge Project(Grant No.TZ2018002);National Science and TechnologyMajor Project(J2019-II-0007-0027);supported by the China Postdoctoral Science Foundation(Grant No.2020M670116);the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202001).; In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation.The quadratic auxiliary variable approach is first pr...; 关键词：Quadratic auxiliary variable approach symplectic Runge-Kutta scheme energypreserving algorithm Fourier pseudo-spectral method

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

Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications: 《Numerical Mathematics(Theory,Methods and Applications)》2022年第2期304-335,共32页Geng Sun Siqing Gan Hongyu Liu Zaijiu Shang; supported by the NSF of China(No.11771436);The work of S.Gan was supported by the NSF of China,No.11971488;The work of H.Liu was supported by the Hong Kong RGC General Research Funds,12301218,12302919 and 12301420;The work of Z.Shang was supported by the NSF of China,No.11671392.; Symmetric and symplectic methods are classical notions in the theory of numerical methods for solving ordinary differential equations.They can generate numerical flows that respectively preserve the symmetry and sympl...; 关键词：Runge-Kutta method SYMMETRIC SYMPLECTIC ADJOINT HIGH-ORDER explicit method

Production of the Reduction Formula of Seventh Order Runge-Kutta Method with Step Size Control of an Ordinary Differential Equation: 《Applied Mathematics》2022年第4期325-337,共13页Georgios D. Trikkaliotis Maria Ch. Gousidou-Koutita; The purpose of the present work is to construct a nonlinear equation system (85 × 53) using Butcher’s Table and then by solving this system to find the values of all set parameters and finally the reduction formula ...; 关键词：Initial Value Problem Runge-Kutta Methods Ordinary Differential Equations

Derivation of the Reduction Formula of Sixth Order and Seven Stages Runge-Kutta Method for the Solution of an Ordinary Differential Equation: 《Applied Mathematics》2022年第4期338-355,共18页Georgios D. Trikkaliotis Maria Ch. Gousidou-Koutita; This paper is describing in detail the way we define the equations which give the formulas in the methods Runge-Kutta 6^th order 7 stages with the incorporated control step size in the numerical solution of ...; 关键词：Initial Value Problem Runge-Kutta Methods Ordinary Differential Equations

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