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Applied Numerical Mathematics最新文献

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A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.005
Carmelo Clavero , Shashikant Kumar , Sunil Kumar
{"title":"A priori and a posteriori error estimates for efficient numerical schemes for coupled systems of linear and nonlinear singularly perturbed initial-value problems","authors":"Carmelo Clavero ,&nbsp;Shashikant Kumar ,&nbsp;Sunil Kumar","doi":"10.1016/j.apnum.2024.10.005","DOIUrl":"10.1016/j.apnum.2024.10.005","url":null,"abstract":"<div><div>This work considers the numerical approximation of linear and nonlinear singularly perturbed initial value coupled systems of first-order, for which the diffusion parameters at each equation of the system are distinct and also they can have a different order of magnitude. To do that, we use two efficient discretization methods, which combine the backward differences and an appropriate splitting by components. Both a priori and a posteriori error estimates are proved for the proposed discretization methods. The developed numerical methods are more computationally efficient than those classical methods used to solve the same type of coupled systems. Extensive numerical experiments strongly confirm in practice the theoretical results and corroborate the superior performance of the current approach compared with previous existing approaches.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 123-147"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multilinear algebra methods for higher-dimensional graphs 高维图的多重线性代数方法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.11.009
Alaeddine Zahir , Khalide Jbilou , Ahmed Ratnani
{"title":"Multilinear algebra methods for higher-dimensional graphs","authors":"Alaeddine Zahir ,&nbsp;Khalide Jbilou ,&nbsp;Ahmed Ratnani","doi":"10.1016/j.apnum.2023.11.009","DOIUrl":"10.1016/j.apnum.2023.11.009","url":null,"abstract":"<div><div>In this paper, we will explore the use of multilinear algebra-based methods for higher dimensional graphs. Multi-view clustering (MVC) has gained popularity over the single-view clustering due to its ability to provide more comprehensive insights into the data. However, this approach also presents challenges, particularly in combining and utilizing multiple views or features effectively. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will report on experiments conducted using benchmark datasets to evaluate the performance of the main clustering methods.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 390-407"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted chained graphs and some applications 加权链图和一些应用
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.017
C. Fenu , L. Reichel , G. Rodriguez , Y. Zhang
{"title":"Weighted chained graphs and some applications","authors":"C. Fenu ,&nbsp;L. Reichel ,&nbsp;G. Rodriguez ,&nbsp;Y. Zhang","doi":"10.1016/j.apnum.2023.12.017","DOIUrl":"10.1016/j.apnum.2023.12.017","url":null,"abstract":"<div><div>This paper introduces weighted chained graphs, as well as minimal broadcasting and receiving sets, and investigates their properties. Both directed and undirected graphs are considered. The notion of central nodes is introduced both for weighted directed and undirected graphs. This notion is helpful for determining how quickly information can propagate throughout a graph. In particular, it is useful for the investigation of transportation networks and for city planning. Applications to the analysis of airline and bus networks are presented.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 232-245"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139104446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Multi-Quadrics quasi-interpolation scheme for numerical solution of Burgers' equation
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.025
JiHong Zhang, JiaLi Yu
{"title":"A Multi-Quadrics quasi-interpolation scheme for numerical solution of Burgers' equation","authors":"JiHong Zhang,&nbsp;JiaLi Yu","doi":"10.1016/j.apnum.2024.09.025","DOIUrl":"10.1016/j.apnum.2024.09.025","url":null,"abstract":"<div><div>The Multi-Quadrics (MQ) radial basis function (RBF) quasi-interpolant has received widespread attention due to its simplicity and convenience, avoiding the possible ill-conditioning problem that may occur if there are a lot of interpolation points, and being able to directly provide numerical approximation results. We present a new quasi-interpolant <span><math><msub><mi>L</mi><mi>N</mi></msub></math></span> for scattered data and prove that it has the property of linear reproducing and high computational accuracy, and does not require the first derivative values at the two endpoints, making it easier to use. Finally, the numerical scheme for solving Burgers’ equation is presented, and numerical experiments are carried out and compared with other methods. The numerical results verify the effectiveness and accuracy of the new quasi-interpolant <span><math><msub><mi>L</mi><mi>N</mi></msub></math></span>.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 38-44"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On an algorithm for the numerical solution of quasilinear integral-algebraic equations
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.008
Mikhail Bulatov , Tatiana Indutskaya , Liubov Solovarova
{"title":"On an algorithm for the numerical solution of quasilinear integral-algebraic equations","authors":"Mikhail Bulatov ,&nbsp;Tatiana Indutskaya ,&nbsp;Liubov Solovarova","doi":"10.1016/j.apnum.2024.10.008","DOIUrl":"10.1016/j.apnum.2024.10.008","url":null,"abstract":"<div><div>This article addresses interrelated integral nonlinear Volterra equations of the first and second kinds. Combining them, we obtain a system of integral equations with an identically degenerate matrix multiplying by the main part, which is usually called integral-algebraic equations. We highlight the fundamental features of the problems under consideration, namely their ill-posedness. We give conditions for the existence of a unique sufficiently smooth solution in terms of matrix pencils and propose an algorithm for their numerical solution, which is based on the simplest quadrature formula and linearization of a nonlinear integrand. Illustrative examples and results of numerical calculations of test examples are given.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 348-355"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical differentiation of the piecewise smooth function by using Fourier extension method
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.026
Zhenyu Zhao , Kai Yu , Xianzheng Jia , Zhihong Dou
{"title":"Numerical differentiation of the piecewise smooth function by using Fourier extension method","authors":"Zhenyu Zhao ,&nbsp;Kai Yu ,&nbsp;Xianzheng Jia ,&nbsp;Zhihong Dou","doi":"10.1016/j.apnum.2024.09.026","DOIUrl":"10.1016/j.apnum.2024.09.026","url":null,"abstract":"<div><div>Numerical differentiation of the piecewise smooth function is considered in this paper. To avoid the large error of numerical differentiation that may occur near potential non-smooth points, we identify the discontinuity points of the first or second derivative of the function. Then we divide the domain of the function into several sub-domains. For each sub-domain, the approximation is constructed by Fourier extension, and the global approximation of the piecewise smooth function is formed by superposition to improve accuracy. Some numerical experiments are conducted to further verify the efficacy of the method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 45-57"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An explicit substructuring method for overlapping domain decomposition based on stochastic calculus 基于随机微积分的重叠域分解显式子结构方法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.02.011
Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki
{"title":"An explicit substructuring method for overlapping domain decomposition based on stochastic calculus","authors":"Jorge Morón-Vidal,&nbsp;Francisco Bernal,&nbsp;Atsushi Suzuki","doi":"10.1016/j.apnum.2024.02.011","DOIUrl":"10.1016/j.apnum.2024.02.011","url":null,"abstract":"<div><div>In a recent paper <span><span>[7]</span></span>, a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton, the hybrid approach produces an explicit and sparse shrunken matrix—hence suitable for substructuring again. The ultimate goal is to push strong scalability beyond the state of the art by leveraging the potential for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and—crucially—for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler, and more accurate while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 340-355"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Crank-Nicolson weak Galerkin finite element methods for the sine-Gordon equation
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-01-29 DOI: 10.1016/j.apnum.2025.01.016
Ahmed Al-Taweel , Jumana Alkhalissi , Xiaoshen Wang
{"title":"The Crank-Nicolson weak Galerkin finite element methods for the sine-Gordon equation","authors":"Ahmed Al-Taweel ,&nbsp;Jumana Alkhalissi ,&nbsp;Xiaoshen Wang","doi":"10.1016/j.apnum.2025.01.016","DOIUrl":"10.1016/j.apnum.2025.01.016","url":null,"abstract":"<div><div>This article proposes an efficient second-order weak Galerkin (WG) finite element scheme for solving the 2D damped and undamped sine-Gordon problem with Dirichlet boundary conditions and initial conditions. We also construct and study a fully discrete WG finite element method for solving the sine-Gordon equation with a damping term using the Crank–Nicolson (CN) and Euler schemes. Stability and error analyses are established on a triangular grid for the constructed schemes in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms for the fully discrete and semi-discrete formulation. Our formulation is accurate in space and time. Finally, numerical experiments are performed to validate the theoretical conclusions.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 77-91"},"PeriodicalIF":2.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral element method for the solution of viscoelastic seismic wave propagation
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-01-27 DOI: 10.1016/j.apnum.2025.01.015
Feze Barzegar, Jalil Rashidinia
{"title":"Spectral element method for the solution of viscoelastic seismic wave propagation","authors":"Feze Barzegar,&nbsp;Jalil Rashidinia","doi":"10.1016/j.apnum.2025.01.015","DOIUrl":"10.1016/j.apnum.2025.01.015","url":null,"abstract":"<div><div>This paper considers the Gauss–Legendre–Lobatto spectral element method combined with the Crank–Nicolson (CN) technique to solve the viscoelastic wave equation model. The CN technique is chosen for its unconditional stability and second-order accuracy. Additionally, the convergence order is determined for the time semi-discrete scheme of the problem. The Gauss–Legendre–Lobatto points are used as interpolation nodes and integral quadrature points to discretize the spatial direction with the spectral element method, providing an a priori estimate. Numerical results demonstrate the proposed method's high efficiency and accuracy.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 92-109"},"PeriodicalIF":2.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Error estimates of implicit-explicit compact BDF2 schemes for the pseudo parabolic equations with logarithmic nonlinearity
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.apnum.2025.01.010
Qifeng Zhang , Haiyan Cao , Hongyu Qin
{"title":"Error estimates of implicit-explicit compact BDF2 schemes for the pseudo parabolic equations with logarithmic nonlinearity","authors":"Qifeng Zhang ,&nbsp;Haiyan Cao ,&nbsp;Hongyu Qin","doi":"10.1016/j.apnum.2025.01.010","DOIUrl":"10.1016/j.apnum.2025.01.010","url":null,"abstract":"<div><div>In this paper, two classes of linearized difference schemes are presented for the one and two-dimensional pseudo parabolic equations with logarithmic nonlinearity. These schemes are derived based on the implicit-explicit second-order backward differential formula (BDF2) for the temporal discretization and fourth-order compact/second-order difference schemes for spatial discretization. With the help of the truncation function method and regularization technique, error estimates for the logarithmic nonlinear term are handled rigorously. As a result, the convergence of the fully-discrete schemes is obtained based on the energy argument. Extensive numerical examples are presented to confirm the theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 135-154"},"PeriodicalIF":2.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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