{"title":"Orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method for large-scale linear systems","authors":"Xin-Fang Zhang , Meng-Long Xiao , Zhuo-Heng He","doi":"10.1016/j.aml.2025.109529","DOIUrl":"10.1016/j.aml.2025.109529","url":null,"abstract":"<div><div>Kacamarz-type inner-iteration preconditioned flexible GMRES method, which was proposed by Du et al. (2021), is attractive for solving consistent linear systems. However, its inner iteration was only performed by several commonly used Kaczmarz-type methods, and required computing <span><math><mrow><mi>A</mi><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup></mrow></math></span> in advance, which is unfavorable for big data problems. To overcome these difficulties, we first propose a simple orthogonal block Kaczmarz method, based on the orthogonal block idea without preconditioning, which converges much faster than the mentioned-above Kaczmarz-type solvers. We then derive a simple orthogonal block Kaczmarz inner-iteration preconditioned flexible GMRES method, based on the orthogonal block Kaczmarz inner-iteration as a preconditioner, which is appealing for large-scale linear systems. The convergence analysis of which is also established. Finally, we provide some numerical examples to illustrate the effectiveness of the proposed methods compared with some state-of-the-art Kaczmarz-type methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109529"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551291","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}
{"title":"Global solutions for the system of a viscous two-fluid model","authors":"Yan Liu, Wenjun Wang","doi":"10.1016/j.aml.2025.109530","DOIUrl":"10.1016/j.aml.2025.109530","url":null,"abstract":"<div><div>In this paper, we consider a viscous compressible two-fluid model with a pressure law that depends on two variables. We establish the existence theory for the global solution of this system within the <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-framework <span><math><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span>, assuming that the <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the initial perturbation is small. The energy method combined with the low-frequency and high-frequency decomposition is used to derive the decay of the solution and hence the global existence. As a byproduct, we obtain the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-<span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> convergence rates for the solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109530"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551288","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}
{"title":"On a nonautonomous nonlinear model for cell growth and division","authors":"Qihua Huang, Jie Ou, Xiumei Deng","doi":"10.1016/j.aml.2025.109528","DOIUrl":"10.1016/j.aml.2025.109528","url":null,"abstract":"<div><div>In this paper, we propose and analyze a nonautonomous, nonlinear size-structured population model that describes the growth and division of cells. By applying the monotone method based on a comparison principle, we establish the well-posedness of the model. We then investigate the long-term behavior of the solution using the upper–lower solution approach. Specifically, we derive conditions on the model parameters that determine the persistence or extinction of the cell population.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109528"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551294","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}
{"title":"Global existence and boundedness of classical solutions in chemotaxis-(Navier-)Stokes system with singular sensitivity and self-consistent term","authors":"Yuying Wang, Liqiong Pu, Jiashan Zheng","doi":"10.1016/j.aml.2025.109518","DOIUrl":"10.1016/j.aml.2025.109518","url":null,"abstract":"<div><div>This paper addresses the global existence and boundedness of classical solutions to the Neumann-Neumann-Dirichlet value problem for the chemotaxis system, as described by <span><span><span>(*)</span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>n</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>⋅</mi><mo>∇</mo><mi>n</mi><mo>=</mo><mi>Δ</mi><mi>n</mi><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>c</mi></mrow></mfrac><mo>∇</mo><mi>c</mi></mrow></mfenced><mo>+</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>n</mi><mo>∇</mo><mi>ϕ</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>c</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>⋅</mi><mo>∇</mo><mi>c</mi><mo>=</mo><mi>Δ</mi><mi>c</mi><mo>−</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msup><mi>c</mi><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mo>∇</mo><mi>P</mi><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>n</mi><mo>∇</mo><mi>ϕ</mi><mo>+</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>c</mi></mrow></mfrac><mo>∇</mo><mi>c</mi><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mo>∇</mo><mi>⋅</mi><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mrow><mi>∂</mi><mi>n</mi></mrow><mrow><mi>∂</mi><mi>ν</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>∂</mi><mi>c</mi></mrow><mrow><mi>∂</mi><mi>ν</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mo>,</mo><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>∂</mi><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>n</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>c</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a smoothly bounded domain <span><math><mrow><mi>Ω</m","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109518"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551289","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}
{"title":"Generalized finite difference method for dynamics analysis of axially moving beams and plates","authors":"Cuiju Feng , Cong Xie , Maosheng Jiang","doi":"10.1016/j.aml.2025.109526","DOIUrl":"10.1016/j.aml.2025.109526","url":null,"abstract":"<div><div>In this paper, we propose one novel generalized finite difference method(GFDM) for the moving beams and plates problem. Firstly the second-order backward difference formula scheme is used for the time discretization. And the GFDM idea is explored to discrete the space area. The proposed method is easy to code and deal with the complex boundary conditions. The convergence test is presented and agrees with the theoretical analysis. Also, several simulations for moving beams and plates are presented to address for the accuracy of the method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109526"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551290","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}
{"title":"Lattice Boltzmann modeling of the coherent solid–solid transition with elastic effects","authors":"Han Wu , Dongke Sun , Wei Chen , Qingguo Fei","doi":"10.1016/j.aml.2025.109527","DOIUrl":"10.1016/j.aml.2025.109527","url":null,"abstract":"<div><div>A mesoscopic lattice Boltzmann model is proposed to investigate the dynamic evolution of solid-state structures during the hexagonal-to-orthorhombic transition, incorporating the micro-elastic theory. The model enables detailed observation of the morphology of both single- and multi-variant systems. The analytically recovered macroscopic governing equation is fully consistent with the kinetic theory, and the interactions between different domains are well characterized. The strategy opens up a vast range of solid-state phase transitions, particularly those involving multi-phase and multi-domain systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109527"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551338","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}
{"title":"A generalized Nyström method with subspace iteration for low-rank approximations of large-scale nonsymmetric matrices","authors":"Yatian Wang , Nian-Ci Wu , Yuqiu Liu , Hua Xiang","doi":"10.1016/j.aml.2025.109531","DOIUrl":"10.1016/j.aml.2025.109531","url":null,"abstract":"<div><div>In numerical linear algebra, finding the low-rank approximation of large-scale nonsymmetric matrices is a core problem. In this work, we combine the generalized Nyström method and randomized subspace iteration to propose a new low-rank approximation algorithm, which we refer to as the generalized Nyström method with subspace iteration. Moreover, utilizing the projection theory, we perform an in-depth error analysis from a novel perspective and establish the theoretical error bound of the proposed algorithm. Finally, numerical experiments show that our method outperforms the randomized singular value decomposition and generalized Nyström method in accuracy, especially when applied to a matrix with slowly decaying singular values.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109531"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551292","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}
{"title":"Quasi-exponential stability of non-autonomous integro-differential systems with infinite delay","authors":"Liguang Xu , Hongxiao Hu","doi":"10.1016/j.aml.2025.109520","DOIUrl":"10.1016/j.aml.2025.109520","url":null,"abstract":"<div><div>The current article focuses on the quasi-exponential stability analysis of non-autonomous integro-differential systems characterized by infinite delay. By developing a novel generalized Halanay inequality, sufficient conditions for the quasi-exponential stability of non-autonomous integro-differential systems with infinite delay are presented for the systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109520"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526859","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}
{"title":"On bounds for norms and conditioning of Wasserstein metric matrix","authors":"Zhong-Zhi Bai","doi":"10.1016/j.aml.2025.109510","DOIUrl":"10.1016/j.aml.2025.109510","url":null,"abstract":"<div><div>For the Wasserstein-1 metric matrices of one- and two-dimensions, we prove the two guesses about their computational properties, which were proposed by Bai in 2024 (Linear Algebra Appl. 681(2024), 150-186). More specifically, for these matrices we prove their nonsingularity and symmetric positive definiteness, and derive sharper upper bounds on the norms of their inverses and on their condition numbers, under much more relaxed and realistic conditions imposed upon the involved problem and discretization parameters.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109510"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551293","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}
{"title":"Bistable traveling waves of a nonlocal reaction–diffusion model with non-monotone birth pulse","authors":"Binxiang Dai, Yaobin Tang","doi":"10.1016/j.aml.2025.109519","DOIUrl":"10.1016/j.aml.2025.109519","url":null,"abstract":"<div><div>This paper considers a nonlocal reaction–diffusion model with a non-monotone birth pulse and a bistable response term. We define two monotone semiflows and, using the comparison argument, obtain the threshold dynamics between persistence and extinction in bounded domain. Moreover, we apply the asymptotic fixed point theorem to show the existence of bistable traveling wave solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109519"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520749","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
