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A parallel exponential integrator scheme for linear differential equations
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.018
F. Hecht, S.-M. Kaber
{"title":"A parallel exponential integrator scheme for linear differential equations","authors":"F. Hecht,&nbsp;S.-M. Kaber","doi":"10.1016/j.apnum.2024.10.018","DOIUrl":"10.1016/j.apnum.2024.10.018","url":null,"abstract":"<div><div>New approximations of the matrix <em>φ</em> functions are developed. These approximations are rational functions of a specific form allowing simple and accurate schemes for linear systems. Furthermore, these approximations are fully parallelizable. Several tests show the efficiency of the method and its good parallelization properties.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 356-364"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141231","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
Discretization methods and their extrapolations for two-dimensional nonlinear Volterra-Urysohn integral equations
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.006
Sohrab Bazm , Pedro Lima , Somayeh Nemati
{"title":"Discretization methods and their extrapolations for two-dimensional nonlinear Volterra-Urysohn integral equations","authors":"Sohrab Bazm ,&nbsp;Pedro Lima ,&nbsp;Somayeh Nemati","doi":"10.1016/j.apnum.2024.10.006","DOIUrl":"10.1016/j.apnum.2024.10.006","url":null,"abstract":"<div><div>In this paper, a class of nonlinear two-dimensional (2D) integral equations of Volterra type, i.e. Volterra-Urysohn integral equations, is studied. Following the ideas of <span><span>[24]</span></span>, and assuming that the kernels of the integral equation are Lipschitz functions with respect to the dependent variable, the existence and uniqueness of a solution to the integral equation is shown by a technique based on the Picard iterative method. Then, the Euler and trapezoidal discretization methods are used to reduce the solution of the integral equation to the solution of a system of nonlinear algebraic equations. It is proved that the solution of the Euler method has first order convergence to the exact solution of the integral equation while the solution of the trapezoidal method has quadratic convergence. To prove the convergence of the trapezoidal method, a new Gronwall inequality is developed. Some numerical examples are given which confirm our theoretical results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 323-337"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141229","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
Anderson acceleration. Convergence analysis and applications to equilibrium chemistry 安德森加速收敛分析及在平衡化学中的应用
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.01.022
Rawaa Awada , Jérôme Carrayrou , Carole Rosier
{"title":"Anderson acceleration. Convergence analysis and applications to equilibrium chemistry","authors":"Rawaa Awada ,&nbsp;Jérôme Carrayrou ,&nbsp;Carole Rosier","doi":"10.1016/j.apnum.2024.01.022","DOIUrl":"10.1016/j.apnum.2024.01.022","url":null,"abstract":"<div><div><span><span>In this paper, we study theoretically and numerically the Anderson acceleration method. First, we extend the convergence results of Anderson's method for a small depth to general nonlinear cases. More precisely, we prove that the Type-I and Type-II Anderson(1) are locally q-linearly convergent if the </span>fixed point<span> map is a contraction with a Lipschitz constant small enough. We then illustrate the effectiveness of the method by applying it to the resolution of chemical equilibria. This test case has been identified as a challenging one because of the high nonlinearity of the chemical system and stiffness of the transport phenomena. The Newton method (usually Newton-Raphson) has been adopted by quite all the equilibrium and reactive transport codes. But the often ill-conditioned </span></span>Jacobian matrix<span><span> and the choice of a bad initial data can lead to </span>convergence problems<span><span>, especially if solute transport produces sharp concentrations profiles. Here we propose to combine the Anderson acceleration method with a particular formulation of the equilibrium system called the method of positive continued fractions (usually used as preconditioning). As shown by the numerical simulations, this approach makes it possible to considerably improve the robustness of the resolution of chemical equilibria algorithms, especially since it is coupled with a strategy to monitor the depth of the Anderson acceleration method in order to control the </span>condition number.</span></span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 60-75"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657122","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
Parallel cloud solution of large algebraic multivalued systems 大型代数多值系统的并行云解法
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.03.012
M.A. Rahhali , T. Garcia , P. Spiteri
{"title":"Parallel cloud solution of large algebraic multivalued systems","authors":"M.A. Rahhali ,&nbsp;T. Garcia ,&nbsp;P. Spiteri","doi":"10.1016/j.apnum.2024.03.012","DOIUrl":"10.1016/j.apnum.2024.03.012","url":null,"abstract":"<div><div><span>The present paper deals with the resolution on cloud architecture of synchronous and asynchronous iterative parallel algorithms of stationary or evolution variational inequations formulated by a multivalued model. The performances of synchronous and asynchronous iterative parallel methods are compared with previous ones obtained on cluster or when grid architecture is used. Thanks to the properties of the algebraic systems resulting from problem discretization we are able to analyze the behavior of the iterative algorithm in particular the convergence and the speed of convergence. The implementation of the studied methods on cloud architecture is described. Then we present various applications in particular the solidification of steel in </span>continuous casting<span>, the cavity pressure calculation described by a problem subject to unilateral constraints and finally a financial problem modeled by American option pricing.</span></div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 366-389"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196987","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 GPU-accelerated Lagrangian method for solving the Liouville equation in random differential equation systems
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.021
V.J. Bevia, S. Blanes, J.C. Cortés, N. Kopylov, R.J. Villanueva
{"title":"A GPU-accelerated Lagrangian method for solving the Liouville equation in random differential equation systems","authors":"V.J. Bevia,&nbsp;S. Blanes,&nbsp;J.C. Cortés,&nbsp;N. Kopylov,&nbsp;R.J. Villanueva","doi":"10.1016/j.apnum.2024.09.021","DOIUrl":"10.1016/j.apnum.2024.09.021","url":null,"abstract":"<div><div>This work presents and analyzes a numerical approach to efficiently solve the Liouville equation in the context of random ODEs using GPGPUs. Our method combines wavelet compression-based adaptive mesh refinement, Lagrangian particle methods, and radial basis function interpolation to create a versatile algorithm applicable in multiple dimensions. We discuss the advantages and limitations of this algorithm. To demonstrate its effectiveness, we compute the probability density function for various 2D and 3D random ODE systems with applications in physics and epidemiology.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 231-255"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143141232","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
Central composite designs with three missing observations 有三个缺失观测点的中心复合设计
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2023.12.013
K. Alanazi , S.D. Georgiou , C. Koukouvinos , S. Stylianou
{"title":"Central composite designs with three missing observations","authors":"K. Alanazi ,&nbsp;S.D. Georgiou ,&nbsp;C. Koukouvinos ,&nbsp;S. Stylianou","doi":"10.1016/j.apnum.2023.12.013","DOIUrl":"10.1016/j.apnum.2023.12.013","url":null,"abstract":"<div><div>In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and predictive capability of the central composite design (CCD). Therefore minimaxloss CCD is formulated under a minimaxloss criterion. The minimaxloss CCD is considered to be robust to three missing observation and the investigation has been made in this article. The general formulas for the efficiency of the design when missing three observations, are presented in closed form as a function of <em>α</em>, where <em>α</em> is the value used in the CCDs' axial part. For the first time in this paper, these are calculated explicitly for CCDs from <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> to <span><math><mi>k</mi><mo>=</mo><mn>7</mn></math></span> factors and displayed in tables for practitioners to use. The corresponding graphs for the efficiencies are presented and suggestions are made for the values of <em>α</em> to maximize the robustness and estimability of the design for all cases.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 2-21"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069675","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
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
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