Calcolo最新文献 - Book学术

Adaptive finite element approximation of bilinear optimal control problem with fractional Laplacian 带分数拉普拉卡矩的双线性优化控制问题的自适应有限元逼近

IF 1.7 2区数学

Calcolo Pub Date : 2024-09-16 DOI: 10.1007/s10092-024-00611-2

Fangyuan Wang, Qiming Wang, Zhaojie Zhou

引用次数: 0

An explicit two-grid spectral deferred correction method for nonlinear fractional pantograph differential equations 非线性分数受电微分方程的显式双网格光谱延迟修正法

IF 1.7 2区数学

Calcolo Pub Date : 2024-09-16 DOI: 10.1007/s10092-024-00614-z

Shan Li, Cunxuan Du, Zhongqing Wang

引用次数: 0

A modification of the periodic nonuniform sampling involving derivatives with a Gaussian multiplier 用高斯乘法器对涉及导数的周期性非均匀采样进行修改

IF 1.7 2区数学

Calcolo Pub Date : 2024-09-13 DOI: 10.1007/s10092-024-00589-x

Rashad M. Asharabi, Mustafa Q. Khirallah

{"title":"A modification of the periodic nonuniform sampling involving derivatives with a Gaussian multiplier","authors":"Rashad M. Asharabi, Mustafa Q. Khirallah","doi":"10.1007/s10092-024-00589-x","DOIUrl":"https://doi.org/10.1007/s10092-024-00589-x","url":null,"abstract":"The periodic nonuniform sampling series, involving periodic samples of both the function and its first r derivatives, was initially introduced by Nathan (Inform Control 22: 172–182, 1973). Since then, various authors have extended this sampling series in different contexts over the past decades. However, the application of the periodic nonuniform derivative sampling series in approximation theory has been limited due to its slow convergence. In this article, we introduce a modification to the periodic nonuniform sampling involving derivatives by incorporating a Gaussian multiplier. This modification results in a significantly improved convergence rate, which now follows an exponential order. This is a significant improvement compared to the original series, which had a convergence rate of (O(N^{-1/p})) where (p>1). The introduced modification relies on a complex-analytic technique and is applicable to a wide range of functions. Specifically, it is suitable for the class of entire functions of exponential type that satisfy a decay condition, as well as for the class of analytic functions defined on a horizontal strip. To validate the presented theoretical analysis, the paper includes rigorous numerical experiments.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"25 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260835","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

Fast algebraic multigrid for block-structured dense systems arising from nonlocal diffusion problems 非局部扩散问题引起的块状结构密集系统的快速代数多网格计算

IF 1.7 2区数学

Calcolo Pub Date : 2024-09-13 DOI: 10.1007/s10092-024-00612-1

Minghua Chen, Rongjun Cao, Stefano Serra-Capizzano

{"title":"Fast algebraic multigrid for block-structured dense systems arising from nonlocal diffusion problems","authors":"Minghua Chen, Rongjun Cao, Stefano Serra-Capizzano","doi":"10.1007/s10092-024-00612-1","DOIUrl":"https://doi.org/10.1007/s10092-024-00612-1","url":null,"abstract":"Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large structured systems of equations. However, how to build/check restriction and prolongation operators in practical AMG methods for nonsymmetric structured systems is still an interesting open question in its full generality. The present paper deals with the block-structured dense and Toeplitz-like-plus-cross systems, including nonsymmetric indefinite and symmetric positive definite (SPD) ones, arising from nonlocal diffusion problems. The simple (traditional) restriction operator and prolongation operator are employed in order to handle such block-structured dense and Toeplitz-like-plus-cross systems, which are convenient and efficient when employing a fast AMG. We provide a detailed proof of the two-grid convergence of the method for the considered SPD structures. The numerical experiments are performed in order to verify the convergence with a computational cost of only (mathscr {O}(N text{ log } N)) arithmetic operations, by exploiting the fast Fourier transform, where N is the number of the grid points. To the best of our knowledge, this is the first contribution regarding Toeplitz-like-plus-cross linear systems solved by means of a fast AMG.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"31 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260834","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 the positivity of B-spline Wronskians 关于 B-样条线 Wronskians 的实在性

IF 1.7 2区数学

Calcolo Pub Date : 2024-09-10 DOI: 10.1007/s10092-024-00613-0

Michael S. Floater

引用次数: 0

An unconditional boundary and dynamics preserving scheme for the stochastic epidemic model 随机流行病模型的无条件边界和动态保护方案

IF 1.7 2区数学

Calcolo Pub Date : 2024-08-31 DOI: 10.1007/s10092-024-00606-z

Ruishu Liu, Xiaojie Wang, Lei Dai

引用次数: 0

A computational method for singularly perturbed reaction–diffusion type system of integro-differential equations with discontinuous source term 具有不连续源项的奇异扰动反应扩散型积分微分方程系统的计算方法