IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2025-05-27 DOI: 10.1007/s10444-025-10240-0

Cao-Kha Doan, Phuoc-Toan Huynh, Thi-Thao-Phuong Hoang

{"title":"Noniterative localized exponential time differencing methods for hyperbolic conservation laws","authors":"Cao-Kha Doan, Phuoc-Toan Huynh, Thi-Thao-Phuong Hoang","doi":"10.1007/s10444-025-10240-0","DOIUrl":"10.1007/s10444-025-10240-0","url":null,"abstract":"<div><p>The paper is concerned with efficient time discretization methods based on exponential integrators for scalar hyperbolic conservation laws. The model problem is first discretized in space by the discontinuous Galerkin method, resulting in a system of nonlinear ordinary differential equations. To solve such a system, exponential time differencing of order 2 (ETDRK2) is employed with Jacobian linearization at each time step. The scheme is fully explicit and relies on the computation of matrix exponential vector products. To accelerate such computation, we further construct a noniterative, nonoverlapping domain decomposition algorithm, namely localized ETDRK2, which loosely decouples the system at each time step via suitable interface conditions. Temporal error analysis of the proposed global and localized ETDRK2 schemes is rigorously proved; moreover, the schemes are shown to be conservative under periodic boundary conditions. Numerical results for the Burgers’ equation in one and two dimensions (with moving shocks) are presented to verify the theoretical results and illustrate the performance of the global and localized ETDRK2 methods where large time step sizes can be used without affecting numerical stability.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"51 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Nonlinear Schrödinger equations of general form and their exact solutions 一般形式的非线性Schrödinger方程及其精确解

IF 2.9 2区数学

Applied Mathematics Letters Pub Date : 2025-05-27 DOI: 10.1016/j.aml.2025.109622

Nikolay A. Kudryashov , Andrei D. Polyanin

{"title":"Nonlinear Schrödinger equations of general form and their exact solutions","authors":"Nikolay A. Kudryashov , Andrei D. Polyanin","doi":"10.1016/j.aml.2025.109622","DOIUrl":"10.1016/j.aml.2025.109622","url":null,"abstract":"<div><div>The wide class of nonlinear Schrödinger equation of the general form is studied. These nonlinear partial differential equations, depending on arbitrary functions, are not integrable by the inverse scattering transform but have exact solutions. The approach is proposed that makes it possible to find nonlinear Schrodinger equations of the general form that have exact solutions. This approach is that the solutions of nonlinear Schrödinger equations are expressed in a special way through the solutions of auxiliary nonlinear ordinary differential equations of the second order. In this case, one constraint is imposed on three arbitrary functions that determine the class of nonlinear partial differential equations under consideration. A number of new nonlinear Schrödinger equations are presented, which admit generalized traveling wave solutions expressed in terms of elementary and elliptic functions. The described new approach and exact solutions can be used as test problems intended to assess the accuracy of numerical and approximate analytical methods for solving complex nonlinear partial differential equations of mathematical physics.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"170 ","pages":"Article 109622"},"PeriodicalIF":2.9,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147120","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

Symmetric and exterior squares of hook representations 钩子表示的对称和外部正方形

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2025-05-27 DOI: 10.1016/j.jpaa.2025.108003

Szabolcs Mészáros , János Wolosz

引用次数: 0

Characterization of the OU matrix of a braid diagram 编织图的OU矩阵的表征

IF 0.6 4区数学

Topology and its Applications Pub Date : 2025-05-27 DOI: 10.1016/j.topol.2025.109440

Ayaka Shimizu , Yoshiro Yaguchi

引用次数: 0

Some observations regarding the stationary Buckley–Leverett equation 关于稳态巴克利-莱弗里特方程的一些观察

IF 2.9 2区数学

Applied Mathematics Letters Pub Date : 2025-05-27 DOI: 10.1016/j.aml.2025.109621

G.M. Coclite , K.H. Karlsen , N.H. Risebro

引用次数: 0

Weak-strong uniqueness for a specific class of cross-diffusion models with volume filling 一类具有体积填充的交叉扩散模型的弱-强唯一性

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-27 DOI: 10.1016/j.jmaa.2025.129727

Ling Liu

引用次数: 0

Analysis of an HIV/AIDS Model with sexual transmission and travel in a patchy environment. 局部环境下具有性传播和传播的HIV/AIDS模型分析

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-27 DOI: 10.1007/s00285-025-02226-9

Juping Zhang, Xueyan Ma, Zhen Jin

{"title":"Analysis of an HIV/AIDS Model with sexual transmission and travel in a patchy environment.","authors":"Juping Zhang, Xueyan Ma, Zhen Jin","doi":"10.1007/s00285-025-02226-9","DOIUrl":"https://doi.org/10.1007/s00285-025-02226-9","url":null,"abstract":"<p><p>In this paper, a multi-patch HIV/AIDS epidemic model with heterosexual transmission is formulated to investigate the impact of travel among patches. It is a system of <math><mrow><mn>6</mn> <msup><mi>n</mi> <mn>2</mn></msup> </mrow> </math> ordinary differential equations describes HIV/AIDS spread in an environment divided into n patches. We derive the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . Lower and upper bounds on <math><msub><mi>R</mi> <mn>0</mn></msub> </math> are given. We prove that if <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> , the disease-free equilibrium is locally asymptotically stable, and if <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> , there is at least an endemic equilibrium. We apply the model to three patches in which the disease spreads in a patch and dies out in the other two patches when there is no travel between them. We considered three types of connection between three patches: full connection(FC), i.e., <math><mrow><mn>1</mn> <mo>⇔</mo> <mn>2</mn> <mo>⇔</mo> <mn>3</mn> <mo>⇔</mo> <mn>1</mn></mrow> </math> , circular connection(CC), i.e., <math><mrow><mn>1</mn> <mo>↔</mo> <mn>2</mn> <mo>↔</mo> <mn>3</mn> <mo>↔</mo> <mn>1</mn></mrow> </math> and bidirectional connection(BC), i.e., <math><mrow><mn>1</mn> <mo>⇔</mo> <mn>2</mn> <mo>⇔</mo> <mn>3</mn></mrow> </math> . We set different travel and return rates to study the impact of travel on the spread of HIV/AIDS. Numerical simulations confirm the theoretical results and indicate that travel may increase or decrease the spread of HIV/AIDS, i.e. HIV/AIDS may become endemic or die out in three patches when travel occurs, and three types of connection may have different impacts on disease transmission.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 1","pages":"2"},"PeriodicalIF":2.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144163599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Finite-time stabilization of a class of unbounded parabolic bilinear systems in Hilbert space Hilbert空间中一类无界抛物型双线性系统的有限时间镇定

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-27 DOI: 10.1016/j.jmaa.2025.129720

Younes Amaliki, Mohamed Ouzahra

引用次数: 0

A class of time-dependent mixed quasi-variational–hemivariational inequality problems: solvability and applications 一类时变混合拟变分-半变分不等式问题：可解性及其应用

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-05-27 DOI: 10.1016/j.cnsns.2025.108966

Chang Wang , Yi-bin Xiao , Dong-ling Cai

引用次数: 0

Bifurcations induced by nonlocal spatial memory versus nonlocal perception. 非局部空间记忆与非局部知觉诱导的分岔。

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2025-05-27 DOI: 10.1007/s00285-025-02234-9

Yujia Wang, Yongli Song, Hao Wang

{"title":"Bifurcations induced by nonlocal spatial memory versus nonlocal perception.","authors":"Yujia Wang, Yongli Song, Hao Wang","doi":"10.1007/s00285-025-02234-9","DOIUrl":"https://doi.org/10.1007/s00285-025-02234-9","url":null,"abstract":"<p><p>Spatial memory and perception are two key mechanisms driving animal movement's decisions. In this paper, we formulate a reaction-diffusion model incorporating nonlocal spatial memory and nonlocal perception with both kernels characterized by a top-hat function. To understand the impact of species' memory and instantaneous perception on their movement, we investigate how memory-induced diffusion coefficient, perceptual strength, memory delay, and perceptual scale affect the stability and spatiotemporal dynamics of positive steady states. For spatial memory versus perception, we sketch bifurcation curves in the planes of memory delay and perception scale. When memory and perception are weak, the positive constant steady state remains locally asymptotically stable, indicating minimal impact on stability. A larger perception scale preserves stability, whereas a smaller one can induce instability through bifurcations. Specifically, when both the memory-induced diffusion coefficient and perceptual strength are large and share the same sign (or differ in sign), the system undergoes Turing bifurcation to produce spatially nonhomogeneous steady states (or spatially nonhomogeneous periodic solutions via Hopf bifurcation with increased memory delay). When one of these two parameters is large and the other is small, the stability boundary of the positive constant steady state may be governed by Turing bifurcation or a combination of Turing and Hopf bifurcations, potentially leading to higher codimension bifurcations such as Turing-Hopf and Hopf-Hopf bifurcations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 1","pages":"3"},"PeriodicalIF":2.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144163603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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