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Stability analysis of linear fractional neutral delay differential equations 线性分数中性延迟微分方程的稳定性分析
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-24 DOI: 10.1007/s10092-024-00595-z
Jingjun Zhao, Xingchi Wang, Yang Xu
{"title":"Stability analysis of linear fractional neutral delay differential equations","authors":"Jingjun Zhao, Xingchi Wang, Yang Xu","doi":"10.1007/s10092-024-00595-z","DOIUrl":"https://doi.org/10.1007/s10092-024-00595-z","url":null,"abstract":"<p>This paper investigates the analytical stability region and the asymptotic stability of linear fractional neutral delay differential equations. Employing boundary locus techniques, the stability region of this problem is analyzed. Furthermore, we derive the fundamental solution of linear fractional neutral delay differential equations, and prove the exponential boundedness, the asymptotic stability and the algebraic decay rate. Finally, numerical tests are conducted to verify the theoretical results.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500848","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
Fredholm integral equations with non-smooth kernels in weighted spaces: Nyström approximations, stability and convergence 加权空间中具有非光滑核的弗雷德霍姆积分方程：尼斯特伦近似、稳定性和收敛性
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-19 DOI: 10.1007/s10092-024-00593-1
Chafik Allouch
{"title":"Fredholm integral equations with non-smooth kernels in weighted spaces: Nyström approximations, stability and convergence","authors":"Chafik Allouch","doi":"10.1007/s10092-024-00593-1","DOIUrl":"https://doi.org/10.1007/s10092-024-00593-1","url":null,"abstract":"<p>This paper deals with the numerical solution of <i>Fredholm</i> integral equations of the second kind with endpoint algebraic singularities and with a kernel of <i>Green</i>’s function type. Novel <i>Nyström</i> schemes employing the <i>Gauss</i> quadrature rule are presented. These methods take into account the lack of smoothness along the diagonal of the kernel and may recover the full convergence rate of smooth kernels. A complete analysis of the stability and convergence is provided, and several numerical tests that illustrate the efficiency and accuracy of various approaches are considered.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500922","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
Existence of smooth solutions to the 3D Navier–Stokes equations based on numerical solutions by the Crank–Nicolson finite element method 基于克兰克-尼科尔森有限元法数值解的三维纳维-斯托克斯方程光滑解的存在性
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-13 DOI: 10.1007/s10092-024-00590-4
Wentao Cai, Mingyan Zhang
{"title":"Existence of smooth solutions to the 3D Navier–Stokes equations based on numerical solutions by the Crank–Nicolson finite element method","authors":"Wentao Cai, Mingyan Zhang","doi":"10.1007/s10092-024-00590-4","DOIUrl":"https://doi.org/10.1007/s10092-024-00590-4","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141348647","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
When rational functions meet virtual elements: the lightning virtual element method 当有理函数遇到虚元：闪电虚元法
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-13 DOI: 10.1007/s10092-024-00585-1
Manuel Trezzi, Umberto Zerbinati
{"title":"When rational functions meet virtual elements: the lightning virtual element method","authors":"Manuel Trezzi, Umberto Zerbinati","doi":"10.1007/s10092-024-00585-1","DOIUrl":"https://doi.org/10.1007/s10092-024-00585-1","url":null,"abstract":"<p>We propose a lightning Virtual Element Method that eliminates the stabilisation term by actually computing the virtual component of the local VEM basis functions using a lightning approximation. In particular, the lightning VEM approximates the virtual part of the basis functions using rational functions with poles clustered exponentially close to the corners of each element of the polygonal tessellation. This results in two great advantages. First, the mathematical analysis of a priori error estimates is much easier and essentially identical to the one for any other non-conforming Galerkin discretisation. Second, the fact that the lightning VEM truly computes the basis functions allows the user to access the point-wise value of the numerical solution without needing any reconstruction techniques. The cost of the local construction of the VEM basis is the implementation price that one has to pay for the advantages of the lightning VEM method, but the embarrassingly parallelizable nature of this operation will ultimately result in a cost-efficient scheme almost comparable to standard VEM and FEM.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500849","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 discontinuous Galerkin method for Maxwell’s transmission eigenvalue problem 麦克斯韦传输特征值问题的非连续伽勒金方法
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-13 DOI: 10.1007/s10092-024-00583-3
Jiayu Han
{"title":"A discontinuous Galerkin method for Maxwell’s transmission eigenvalue problem","authors":"Jiayu Han","doi":"10.1007/s10092-024-00583-3","DOIUrl":"https://doi.org/10.1007/s10092-024-00583-3","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141346936","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 tensor spectral $${textbf{p}}$$-norm and its higher order power method 关于张量谱$${textbf{p}}$规范及其高阶幂方法
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-13 DOI: 10.1007/s10092-024-00588-y
Chao Zeng
{"title":"On the tensor spectral $${textbf{p}}$$-norm and its higher order power method","authors":"Chao Zeng","doi":"10.1007/s10092-024-00588-y","DOIUrl":"https://doi.org/10.1007/s10092-024-00588-y","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141346829","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 bounds on the Crouzeix ratio for a class of matrices 一类矩阵的 Crouzeix 比率数值界限
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-08 DOI: 10.1007/s10092-024-00580-6
Michel Crouzeix, Anne Greenbaum, Kenan Li
{"title":"Numerical bounds on the Crouzeix ratio for a class of matrices","authors":"Michel Crouzeix, Anne Greenbaum, Kenan Li","doi":"10.1007/s10092-024-00580-6","DOIUrl":"https://doi.org/10.1007/s10092-024-00580-6","url":null,"abstract":"<p>We provide numerical bounds on the Crouzeix ratio for KMS matrices <i>A</i> which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all polynomials <i>p</i> of the spectral norm of <i>p</i>(<i>A</i>) divided by the maximum absolute value of <i>p</i> on the numerical range of <i>A</i>. Our bounds satisfy the conjecture that this ratio is less than or equal to 2. We also give a precise description of these numerical ranges.\u0000</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549740","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 block quaternion GMRES method and its convergence analysis 分块四元数 GMRES 方法及其收敛性分析
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-08 DOI: 10.1007/s10092-024-00576-2
Sinem Şimşek
{"title":"A block quaternion GMRES method and its convergence analysis","authors":"Sinem Şimşek","doi":"10.1007/s10092-024-00576-2","DOIUrl":"https://doi.org/10.1007/s10092-024-00576-2","url":null,"abstract":"<p>We consider the quaternion linear system <span>(AX = B)</span> for the unknown matrix <i>X</i>, where <i>A</i>, <i>B</i> are given <span>(ntimes n)</span>, <span>(ntimes s)</span> matrices with quaternion entries, motivated by applications that arise from fields such as quantum mechanics and signal processing. Our primary concern is the large-scale setting when <i>n</i> is large so that direct solutions are not feasible. We describe a block Krylov subspace method for the iterative solution of these quaternion linear systems. One difference compared to usual block Krylov subspace methods over complex Euclidean spaces is that the multiplication of quaternion scalars is not commutative. We describe a block quaternion Arnoldi process, taking noncommutativity features of quaternions into account, to generate an orthonormal basis for the quaternion Krylov space <span>(text {blockspan} { R_0, A R_0, dots , A^k R_0 })</span>, where <span>(R_0 = B - A X_0)</span> and <span>(X_0)</span> is an initial guess for the solution. Then the best solution of <span>(AX = B)</span> in the least-squares sense is sought in the generated Krylov space. We explain how these least-squares problems over quaternion Krylov spaces can be solved efficiently by means of Householder reflectors. Most notably, we analyze rigorously the convergence of the proposed block quaternion GMRES approach when <i>A</i> is diagonalizable, and in the more general setting when <i>A</i> is not necessarily diagonalizable by making use of the Jordan form of <i>A</i>. Finally, we report numerical results that confirm the validity of the deduced theoretical convergence results, in particular illustrate that the proposed block quaternion Krylov subspace method converges quickly when <i>A</i> has clustered eigenvalues.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526423","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 convergence of waveform relaxation for nonlinear systems of ordinary differential equations 论非线性常微分方程系统波形松弛的收敛性
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-05 DOI: 10.1007/s10092-024-00578-0
M. A. Botchev
{"title":"On convergence of waveform relaxation for nonlinear systems of ordinary differential equations","authors":"M. A. Botchev","doi":"10.1007/s10092-024-00578-0","DOIUrl":"https://doi.org/10.1007/s10092-024-00578-0","url":null,"abstract":"<p>To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard–Lindelöf iteration), where at each iteration a linear inhomogeneous system of differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepping involved. This approach has recently been shown to be efficient as a time-parallel integrator within the PARAEXP framework. In this paper, convergence behavior of this method is assessed theoretically and practically. We examine efficiency of the method by testing it on nonlinear Burgers, Liouville–Bratu–Gelfand, and nonlinear heat conduction equations and comparing its performance with that of conventional time-stepping integrators.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526424","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
Hosvd-tmpe: an extrapolation method for multidimensional sequences Hosvd-tmpe：多维序列的外推法
IF 1.7 2区 数学
Calcolo Pub Date : 2024-06-03 DOI: 10.1007/s10092-024-00582-4
Abdeslem Hafid Bentbib, Khalid Jbilou, Ridwane Tahiri
{"title":"Hosvd-tmpe: an extrapolation method for multidimensional sequences","authors":"Abdeslem Hafid Bentbib, Khalid Jbilou, Ridwane Tahiri","doi":"10.1007/s10092-024-00582-4","DOIUrl":"https://doi.org/10.1007/s10092-024-00582-4","url":null,"abstract":"<p>Accelerating slowly convergent sequences is one of the main purposes of extrapolation methods. In this paper, we present a new tensor polynomial extrapolation method, which is based on a modified minimisation problem and some ideas leading to the recent Tensor Global Minimal Extrapolation Method (TG-MPE). We discuss the application of our method to fixed-point iterative process. An efficient algorithm via the higher order Singular Value Decomposition (HOSVD) is proposed for its implementation. The numerical tests show clearly the effectiveness and performance of the proposed method.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253697","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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