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国家自然科学基金(91130003): 作品数：14被引量：52H指数：3; 导出分析报告; 相关作者：汤涛周涛吴树林更多>>; 相关机构：香港浸会大学中国科学院数学与系统科学研究院四川理工学院更多>>; 相关期刊：《Science China Mathematics》《Advances in Applied Mathematics and Mechanics》《Journal of Computational Mathematics》《Acta Mathematicae Applicatae Sinica》更多>>; 相关主题：STOCHASTICINTEGRATORSRUNGE-KUTTA_METHODSCONSERVATION_LAWSOLITON更多>>; 相关领域：理学一般工业技术更多>>

A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations被引量：1: 《Communications in Computational Physics》2017年第1期93-125,共33页Chuchu Chen Jialin Hong Lihai Ji Linghua Kong; This work was supported by the National Natural Science Foundation of China(Nos.91530118,91130003,11021101,11290142,11471310,11601032,11301234,11271171);the Provincial Natural Science Foundation of Jiangxi(Nos.20142BCB23009,20161ACB20006,20151BAB201012).; In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation la...; 关键词：Coupled stochastic nonlinear Schrodinger equations compact scheme stochastic multi-symplectic conservation law energy evolution law charge conservation law soliton evolution soliton interaction

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

STRONG PREDICTOR-CORRECTOR APPROXIMATION FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS被引量：3: 《Journal of Computational Mathematics》2015年第6期587-605,共19页Yuanling Niu Chengjian Zhang Kevin Burrage; This work is supported by National Natural Science Foundation of China （Nos. 11401594, 11171125, 91130003） and the New Teachers＇ Specialized Research Fund for the Doctoral Program from Ministry of Education of China （No. 20120162120096）.; This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p...; 关键词：Strong predictor-corrector approximation Stochastic delay differential equa- tions CONVERGENCE Mean-square stability Numerical experiments Vectorised simulation.

不确定性量化的高精度数值方法和理论献给林群教授80华诞被引量：32: 《中国科学：数学》2015年第7期891-928,共38页汤涛周涛; 国家自然科学基金(批准号:91130003和11201461)资助项目; 不确定性量化(uncertainty quantification,UQ)是近年来国际上热门的研究课题,其应用领域包括水文学、流体力学、数据同化和天气预测等.由于UQ问题中的大量随机参数引起的超大计算量,如何设计高效的高精度数值方法变得非常重要,与其相...; 关键词：不确定性量化多项式逼近随机配置方法离散L^2 投影压缩感知正倒向随机微分方程

On the Choice of Design Points for Least Square Polynomial Approximations with Application to Uncertainty Quantification: 《Communications in Computational Physics》2014年第7期365-381,共17页Zhen Gao Tao Zhou; supported by National Natural Science Foundation of China(11201441);the Natural Science Foundation of Shandong Province(ZR2012AQ003);and China Postdoctoral Science Foundation(2012M521374/2013T60684);The second author is supported by the National Natural Science Foundation of China(No.91130003 and No.11201461).; In this work,we concern with the numerical comparison between different kinds of design points in least square(LS)approach on polynomial spaces.Such a topic is motivated by uncertainty quantification(UQ).Three kinds o...; 关键词：Least square polynomial approximations uncertainty quantification condition number.

A Stochastic Collocation Method for Delay Differential Equations with Random Input: 《Advances in Applied Mathematics and Mechanics》2014年第4期403-418,共16页Tao Zhou; the National Natural Science Foundation of China(No.91130003 and No.11201461).; In this work,we concern with the numerical approach for delay differential equations with random coefficients.We first show that the exact solution of the problem considered admits good regularity in the random space,...; 关键词：Delay differential equations stochastic collocation sparse grid legendre spectral method

Quasi-Optimized Overlapping Schwarz Waveform Relaxation Algorithm for PDEs with Time-Delay: 《Communications in Computational Physics》2013年第8期780-800,共21页Shu-Lin Wu Ting-Zhu Huang; supported by the NSF of China(11226312,91130003);the NSF of Sichuan University of Science and Engineering(2012XJKRL005);the Opening Fund of Artificial Intelligence Key Laboratory of Sichuan Province(2011RZY04);the Chinese Universities Specialized Research Fund for the Doctoral Program(20110185110020).; Schwarzwaveformrelaxation(SWR)algorithmhas been investigated deeply and widely for regular time dependent problems.But for time delay problems,complete analysis of the algorithm is rare.In this paper,by using the reac...; 关键词：Schwarz method waveform relaxation time delay min-max problem

Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation被引量：3: 《Communications in Computational Physics》2013年第7期393-411,共19页Shanshan Jiang Lijin Wang Jialin Hong; supported by the NNSFC(No.11001009);supported by the Director Foundation of GUCAS,the NNSFC(No.11071251);supported by the Foundation of CAS and the NNSFC(No.11021101,No.91130003).; In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochas...; 关键词：Stochastic nonlinear Schrodinger equations stochasticmulti-symplectic Hamiltonian systems multi-symplectic integrators

LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates被引量：2: 《Communications in Computational Physics》2013年第6期219-241,共23页Linghua Kong Jialin Hong Jingjing Zhang; supported by the National Natural Science Foundation of China(Nos.10901074,11271171);the Provincial Natural Science Foundation of Jiangxi(No.20114BAB201011);the Foundation of Department of Education Jiangxi Province(No.GJJ12174);the State Key Laboratory of Scientific and Engineering Computing,CAS;supported by the Director Innovation Foundation of ICMSEC and AMSS;the Foundation of CAS;the NNSFC(No.91130003,11021101);the Special Funds for Major State Basic Research Projects of China 2005CB321701;supported by the National Natural Science Foundation of China(No.11126118)。; The local one-dimensional multisymplectic scheme(LOD-MS)is developed for the three-dimensional(3D)Gross-Pitaevskii(GP)equation in Bose-Einstein condensates.The idea is originated from the advantages of multisymplectic...; 关键词：LOD-MS Gross-Pitaevskii equation local one-dimensional method midpoint method conservation laws

Generalized Jacobi-Gauss-Lobatto interpolation: 《Frontiers of Mathematics in China》2013年第4期933-960,共28页Zhengsu WAN Benyu GUO Chengjian ZHANG; This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171125, 11271118, 91130003）, the National Natural Science Foundation of China （Tianyuan Fund for Mathematics, Grant No. 11226170）, the Natural Science Foundation of Hunan Province （Grant No. 13JJ4095）, the Postdoctoral Foundation of China （Grant No. 20100471182）, the Construct Program of the Key Discipline in Hunan Province, and the Key Foundation of Hunan Provincial Education Department （Grant No. 11A043）.; We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order ...; 关键词：Generalized Jacobi-Gauss-Lobatto interpolation pseudospectral method non-uniformly weighted Sobolev space

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