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Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions 具有分数阶Neumann边界条件的二维分数阶耦合方程空间非均匀网格的快速数值研究
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-17 DOI: 10.1016/j.aml.2025.109609
Jiaxue Kang, Wenping Fan, Zhenhao Lu
{"title":"Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions","authors":"Jiaxue Kang,&nbsp;Wenping Fan,&nbsp;Zhenhao Lu","doi":"10.1016/j.aml.2025.109609","DOIUrl":"10.1016/j.aml.2025.109609","url":null,"abstract":"<div><div>In this paper, a study on the fast numerical analysis based on spatial nonuniform grids and inverse problem for the two-dimensional space–time fractional coupled equations with fractional Neumann boundary conditions are conducted. The second order L1<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup></math></span> method combined with the Crank–Nicolson (CN) method in time and the fractional block-centered finite difference (BCFD) method based on spatial nonuniform grids in space are employed. To improve computational efficiency, a fast version fractional BCFD algorithm based on the Krylov subspace iterative methods and the spatial sum-of-exponentials (SOE) technology is also constructed. Besides, to conduct the fractional parameter identification problem for the coupled model, an efficient hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is applied. Numerical example is given to verify the correctness and efficiency of the proposed methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109609"},"PeriodicalIF":2.9,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072693","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
Stationary distribution of a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior 具有额外食物、恐惧效应和反捕食行为的随机反应-扩散捕食者-猎物模型的平稳分布
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-16 DOI: 10.1016/j.aml.2025.109612
Haokun Qi, Jiani Jin, Bing Liu, Baolin Kang
{"title":"Stationary distribution of a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior","authors":"Haokun Qi,&nbsp;Jiani Jin,&nbsp;Bing Liu,&nbsp;Baolin Kang","doi":"10.1016/j.aml.2025.109612","DOIUrl":"10.1016/j.aml.2025.109612","url":null,"abstract":"<div><div>The stationary distribution, as a fundamental concept in stochastic processes, is of great significance for exploring the long-term behavior and stability of populations. In this paper, a stochastic reaction–diffusion predator–prey model with additional food, fear effect and anti-predator behavior is proposed, in which the stochastic fluctuations are characterized by a Ornstein–Uhlenbeck process. We proved the existence and uniqueness of the stationary distribution of the stochastic model by constructing the Lyapunov function. Moreover, this study extends the work of Qi and Liu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109612"},"PeriodicalIF":2.9,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070561","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 positive solution for Klein–Gordon–Maxwell system without subcritical growth and Ambrosetti–Rabinowitz conditions 无亚临界生长Klein-Gordon-Maxwell方程组正解的存在性及Ambrosetti-Rabinowitz条件
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-13 DOI: 10.1016/j.aml.2025.109611
Xin Sun , Yu Duan , Jiu Liu
{"title":"Existence of positive solution for Klein–Gordon–Maxwell system without subcritical growth and Ambrosetti–Rabinowitz conditions","authors":"Xin Sun ,&nbsp;Yu Duan ,&nbsp;Jiu Liu","doi":"10.1016/j.aml.2025.109611","DOIUrl":"10.1016/j.aml.2025.109611","url":null,"abstract":"<div><div>This article concerns the following Klein–Gordon–Maxwell system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>−</mo><mrow><mo>(</mo><mn>2</mn><mi>ω</mi><mo>+</mo><mi>ϕ</mi><mo>)</mo></mrow><mi>ϕ</mi><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>s</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>λ</mi><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mi>Δ</mi><mi>ϕ</mi><mo>=</mo><mrow><mo>(</mo><mi>ω</mi><mo>+</mo><mi>ϕ</mi><mo>)</mo></mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>ω</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is a constant, <span><math><mrow><mn>4</mn><mo>≤</mo><mi>s</mi><mo>&lt;</mo><mn>6</mn></mrow></math></span>, <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> is a parameter. When <span><math><mi>f</mi></math></span> only satisfies suplinear conditions but not satisfies subcritical growth and Ambrosetti–Rabinowitz conditions, the existence of positive solution can be proved via variational methods, Moser iteration and perturbation arguments. Our result unifies both critical or supercritical cases and generalizes and improves the existing ones.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109611"},"PeriodicalIF":2.9,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069230","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
Linear stability analysis of 2D incompressible MHD equations with only magnetic diffusion 仅磁扩散的二维不可压缩MHD方程的线性稳定性分析
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109600
Jitao Liu, Huning Zhang
{"title":"Linear stability analysis of 2D incompressible MHD equations with only magnetic diffusion","authors":"Jitao Liu,&nbsp;Huning Zhang","doi":"10.1016/j.aml.2025.109600","DOIUrl":"10.1016/j.aml.2025.109600","url":null,"abstract":"<div><div>Although many physical experiments and numerical simulations show that the magnetic field can stabilize and inhibit electrically conducting fluids, whether 2D incompressible MHD equations with only magnetic diffusion develop finite time singularities or not is one of the most challenging problems and remains open. Therefore, this issue has always attracted a lot of attention of mathematicians. Due to its linearized system plays a crucial role, to deeper understand the aforesaid issue, in this paper, we make the first attempt to study its linear stability when the magnetic field close to the equilibrium state <span><math><mrow><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> in the periodic domain and ultimately proposed the linear stability condition <span><span>(1.4)</span></span>. To be more precise, we show that the solution of its linearized system will be time-asymptotically stable and converge to the equilibrium state in the algebraic rate via the method of spectral analysis, as long as the integrals in the vertical direction of initial perturbations are zeros.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109600"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941937","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
Threshold of a stochastic single population system with infinite delay and time-varying coefficients 具有无限延迟和时变系数的随机单种群系统的阈值
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109597
Daipeng Kuang , Quanxin Zhu , Kai Liu
{"title":"Threshold of a stochastic single population system with infinite delay and time-varying coefficients","authors":"Daipeng Kuang ,&nbsp;Quanxin Zhu ,&nbsp;Kai Liu","doi":"10.1016/j.aml.2025.109597","DOIUrl":"10.1016/j.aml.2025.109597","url":null,"abstract":"<div><div>This paper focuses on a category of stochastic single population systems. Under mild assumptions, we provide a sufficient condition for the existence of stationary distribution in this system by employing variable substitution and the Krylov–Bogoliubov theorem. Furthermore, we demonstrate its proximity to being the sufficient and necessary condition by examining the system’s extinction.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109597"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934865","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
Local solution becomes global solution as damping coefficient goes to infinity 当阻尼系数趋于无穷时，局部解变为全局解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109599
Jiangbo Han , Caijun Wang , Runzhang Xu , Chao Yang
{"title":"Local solution becomes global solution as damping coefficient goes to infinity","authors":"Jiangbo Han ,&nbsp;Caijun Wang ,&nbsp;Runzhang Xu ,&nbsp;Chao Yang","doi":"10.1016/j.aml.2025.109599","DOIUrl":"10.1016/j.aml.2025.109599","url":null,"abstract":"<div><div>We consider a class of wave equations with strong damping, weak damping and nonlinear source term. By constructing the relationship between the blowup time and the coefficients of strong damping and weak damping, we exhibit and verify an interesting phenomenon that the local solution becomes the global solution as the coefficient of strong damping or weak damping goes to infinity.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109599"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934864","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 novel integral inequality for stability of age-structured epidemic models 年龄结构流行病模型稳定性的一个新的积分不等式
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-10 DOI: 10.1016/j.aml.2025.109598
Jianquan Li , Yuming Chen , Fengqin Zhang , Peijun Zhang
{"title":"A novel integral inequality for stability of age-structured epidemic models","authors":"Jianquan Li ,&nbsp;Yuming Chen ,&nbsp;Fengqin Zhang ,&nbsp;Peijun Zhang","doi":"10.1016/j.aml.2025.109598","DOIUrl":"10.1016/j.aml.2025.109598","url":null,"abstract":"<div><div>In this paper, based on a novel integral inequality and the Lyapunov direct method, we propose a systematic approach to determining the global stability of the endemic steady states of age-structured epidemic models. The inequality makes it convenient to verify the negative (semi-)definiteness of the derivative of a Lyapunov functional candidate. The applicability of this approach is illustrated with two age-structured SI and SEI models.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109598"},"PeriodicalIF":2.9,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934766","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
Supercloseness in a balanced norm of the NIPG method on Bakhvalov-type meshes for a reaction diffusion problem 反应扩散问题bakhvalov型网格NIPG方法平衡范数的超接近性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-09 DOI: 10.1016/j.aml.2025.109594
Jiayu Wang , Xiaowei Liu , Xiaoqi Ma
{"title":"Supercloseness in a balanced norm of the NIPG method on Bakhvalov-type meshes for a reaction diffusion problem","authors":"Jiayu Wang ,&nbsp;Xiaowei Liu ,&nbsp;Xiaoqi Ma","doi":"10.1016/j.aml.2025.109594","DOIUrl":"10.1016/j.aml.2025.109594","url":null,"abstract":"<div><div>For numerical methods applied to singularly perturbed reaction-diffusion problems, the balanced norm has emerged as an effective tool. In this manuscript, we analyze supercloseness properties in the balanced norm for the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. To achieve this, we construct a novel interpolant that combines the Lagrange interpolant and a local weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> projection. Furthermore, by appropriately defining penalty parameters at the nodal points of the Bakhvalov-type mesh, we establish supercloseness of almost order <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> in most cases.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109594"},"PeriodicalIF":2.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941938","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
Solvability of a class of nonlinear system of difference equations with homogeneity 一类具有齐次性的非线性差分方程组的可解性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-05-09 DOI: 10.1016/j.aml.2025.109595
Stevo Stević
{"title":"Solvability of a class of nonlinear system of difference equations with homogeneity","authors":"Stevo Stević","doi":"10.1016/j.aml.2025.109595","DOIUrl":"10.1016/j.aml.2025.109595","url":null,"abstract":"<div><div>We show that the following nonlinear system of difference equations of interest <span><span><span><math><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mrow><mo>(</mo><mi>l</mi><mo>)</mo></mrow></mrow></msubsup><mo>=</mo><mfrac><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>l</mi></mrow></msub><munderover><mrow><mo>∏</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>≠</mo><mi>l</mi></mrow><mrow><mi>k</mi></mrow></munderover><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></mrow></msubsup></mrow><mrow><mi>f</mi><mrow><mo>(</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><mspace></mspace><mi>n</mi><mo>∈</mo><mi>N</mi><mo>,</mo><mspace></mspace><mi>l</mi><mo>=</mo><mover><mrow><mn>1</mn><mo>,</mo><mi>k</mi></mrow><mo>¯</mo></mover><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow><mrow><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></mrow></msubsup><mo>∈</mo><mi>ℂ</mi><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>,</mo></mrow></math></span> <span><math><mrow><mi>j</mi><mo>=</mo><mover><mrow><mn>1</mn><mo>,</mo><mi>k</mi></mrow><mo>¯</mo></mover><mo>,</mo></mrow></math></span> and the function <span><math><mrow><mi>f</mi><mo>:</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>→</mo><mi>ℂ</mi></mrow></math></span> is homogeneous of degree <span><math><mrow><mi>k</mi><mo>−</mo><mn>2</mn></mrow></math></span>, is solvable in a closed form considerably extending some results in the literature.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109595"},"PeriodicalIF":2.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934767","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
Convergence rate of truncated EM method for periodic stochastic differential equations in superlinear scenario 超线性情况下周期随机微分方程的截短EM方法的收敛速度
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2025-04-29 DOI: 10.1016/j.aml.2025.109592
Yongmei Cai
{"title":"Convergence rate of truncated EM method for periodic stochastic differential equations in superlinear scenario","authors":"Yongmei Cai","doi":"10.1016/j.aml.2025.109592","DOIUrl":"10.1016/j.aml.2025.109592","url":null,"abstract":"<div><div>Periodicity has been widely recognised in a variety of areas including biology, finance and control theory. As an important class of non-autonomous SDEs, stochastic differential equations (SDEs) with periodic coefficients have thus been receiving great attention recently. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) method to the superlinear SDEs with periodic coefficients and generate an almost optimal convergence rate of order close to <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>. Due to the typical features of such SDEs including periodicity and super-linearity, this work becomes challenging and non-trivial. Finally our theory is demonstrated by computer simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"169 ","pages":"Article 109592"},"PeriodicalIF":2.9,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891294","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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