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《Numerical Mathematics(Theory,Methods and Applications)》: 作品数：819被引量：529H指数：8; 导出分析报告; 主办单位：南京大学; 最新期次：2024年1期更多>>; 发文主题：CONVERGENCEMETHODNUMERICALANALGORITHM更多>>; 发文领域：理学自动化与计算机技术天文地球电子电信更多>>; 发文基金：国家自然科学基金国家重点基础研究发展计划中国博士后科学基金国家教育部博士点基金更多>>

Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期1-36,共36页Weixiong Yuan Tiegang Liu Bin Zhang Kui Cao Kun Wang; supported by the National Natural Science Foundation of China(Grant No.12001031).; A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling mode...; 关键词：Direct discontinuous Galerkin central difference schemes multidomain hybrid methods viscous terms hyperbolic-parabolic equations

A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期37-68,共32页Raziyeh Erfanifar Masoud Hajarian Khosro Sayevand; funded by Iran National Science Foundation(INSF)under Project No.4013447.; In this study,based on an iterative method to solve nonlinear equations,a third-order convergent iterative method to compute the Moore-Penrose inverse of a tensor with the Einstein product is presented and analyzed.Nu...; 关键词：TENSOR iterative methods Moore-Penrose inverse Einstein product

On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期69-92,共24页Raziyeh Erfanifar Masoud Hajarian Khosro Sayevand; funded by Iran National Science Foundation(INSF)under project No.4013447.; This study aims to investigate the polar decomposition of tensors with the Einstein product for theﬁrst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors wit...; 关键词：Iterative methods Einstein product polar decomposition of a tensor polar factor order of convergence

Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期93-120,共28页C.S.Chen Andreas Karageorghis Min Lei; We apply the local method of fundamental solutions(LMFS)to boundary value problems(BVPs)for the Laplace and homogeneous biharmonic equations in annuli.By appropriately choosing the collocation points,the LMFS discreti...; 关键词：Local method of fundamental solutions Poisson equation biharmonic equation matrix decomposition algorithms fast Fourier transforms

Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期121-144,共24页Zhen Miao Bin Wang Yaolin Jiang; supported by the NSFC(Grants 12371403,12271426);by the Key Research and Development Projects of Shaanxi Province(Grant 2023-YBSF-399).; In this paper,we formulate and analyse a kind of parareal-RKN algo-rithms with energy conservation for Hamiltonian systems.The proposed algorithms are constructed by using the ideas of parareal methods,Runge-Kutta-Nys...; 关键词：Parareal methods Runge-Kutta-Nystrom methods Hamiltonian systems energy conservation

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters被引量：1: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期145-180,共36页Yizhong Sun Jiangshan Wang Haibiao Zheng; The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation costs.Our main objective in this paper is to examine a ph...; 关键词：Scalar auxiliary variable ensemble algorithm random interface-coupled problems implicit-explicit partitioned method data-passing partitioned method

Analysis of Deep Ritz Methods for Semilinear Elliptic Equations: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期181-209,共29页Mo Chen Yuling Jiao Xiliang Lu Pengcheng Song Fengru Wang Jerry Zhijian Yang; supported by the National Key Research and Development Program of China(Grant No.2020YFA0714200);the National Nature Science Foundation of China(Grant Nos.12125103,12071362,12371424,12371441);supported by the Fundamental Research Funds for the Central Universities.The numerical calculations have been done at the Supercomputing Center of Wuhan University.; In this paper,we propose a method for solving semilinear elliptical equa-tions using a ResNet with ReLU2 activations.Firstly,we present a comprehensive formulation based on the penalized variational form of the ellipt...; 关键词：Semilinear elliptic equations Deep Ritz method ReLUMo ResNet convergence rate

Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期210-242,共33页Yu Xiong Yanping Chen Jianwei Zhou Qin Liang; In this paper,we construct,analyze,and numerically validate a family of divergence-free virtual elements for Stokes equations with nonlinear damping on polygonal meshes.The virtual element method is H1-conforming and ...; 关键词：Optimal error estimates DIVERGENCE-FREE virtual element nonlinear damping term.

An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps: 《Numerical Mathematics(Theory,Methods and Applications)》2024年第1期243-274,共32页Yabing Sun Jie Yang Weidong Zhao; supported by the NSF of China(Grant Nos.12071261,12001539,11801320,11831010,12371398);by the National Key R&D Program of China(Grant No.2018YFA0703900);by the NSF of Shandong Province(Grant No.ZR2023MA055);by the NSF of Hunan Province(Grant No.2020JJ5647);by the China Postdoctoral Science Foundation(Grant No.2019TQ0073).; In this work,we propose an explicit second order scheme for decoupled mean-ﬁeld forward backward stochastic differential equations with jumps.The sta-bility and the rigorous error estimates are presented,which show th...; 关键词：Mean-field forward backward stochastic differential equation with jumps stability analysis error estimates

Space-Time Decomposition of Kalman Filter: 《Numerical Mathematics(Theory,Methods and Applications)》2023年第4期847-882,共36页Luisa D’Amore Rosalba Cacciapuoti; We present an innovative interpretation of Kalman filter(KF)combining the ideas of Schwarz domain decomposition(DD)and parallel in time(PinT)approaches.Thereafter we call it DD-KF.In contrast to standard DD approaches...; 关键词：Data assimilation Kalman filter domain decomposition filter localization model reduction numerical algorithm

《Numerical Mathematics(Theory,Methods and Applications)》