Mathematical Methods in the Applied Sciences最新文献_第5页

On “From Halley to Secant: Redefining Root Finding With Memory-Based Methods Including Convergence and Stability” 关于“从哈雷到割线：用包括收敛性和稳定性在内的基于记忆的方法重新定义寻根”

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-04 DOI: 10.1002/mma.10861

Arif Rafiq

引用次数: 0

Local Discontinuous Galerkin Method for Solving Compound Nonlinear KdV-Burgers Equations 求解复合非线性KdV-Burgers方程的局部不连续伽辽金法

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-04 DOI: 10.1002/mma.10851

Abhilash Chand, Jugal Mohapatra

{"title":"Local Discontinuous Galerkin Method for Solving Compound Nonlinear KdV-Burgers Equations","authors":"Abhilash Chand, Jugal Mohapatra","doi":"10.1002/mma.10851","DOIUrl":"https://doi.org/10.1002/mma.10851","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, an efficient local discontinuous Galerkin scheme is applied to numerically solve the nonlinear compound KdV-Burgers equation. The numerical scheme utilizes a local discontinuous Galerkin discretization technique in the spatial direction coupled with a higher order strong-stability-preserving Runge–Kutta scheme in the temporal direction. The \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}&#x0005E;2 $$</annotation>\u0000 </semantics></math> stability analysis of the implemented numerical scheme, along with a detailed error estimate for smooth solutions, are also established by carefully selecting the interface numerical fluxes. In addition, numerical simulations are carried out using several illustrative examples, and the results obtained are then compared with solutions acquired by the analytical \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>exp</mi>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>Φ</mi>\u0000 <mo>(</mo>\u0000 <mi>ξ</mi>\u0000 <mo>)</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ exp left(-Phi left(xi right)right) $$</annotation>\u0000 </semantics></math>-expansion method to validate the acceptable accuracy and plausibility of the proposed numerical technique. Also, both two-dimensional and three-dimensional graphical representations are presented to visually demonstrate the physical significance of the resulting traveling wave solutions.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9887-9900"},"PeriodicalIF":2.1,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950160","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

Hybrid Effects of Cooperative Hunting and Inner Fear on the Dynamics of a Fishery Model With Additional Food Supplement 有额外食物补充的渔业模型中，合作狩猎和内心恐惧的混合效应

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10805

Xinrui Yan, Yuan Tian, Kaibiao Sun

{"title":"Hybrid Effects of Cooperative Hunting and Inner Fear on the Dynamics of a Fishery Model With Additional Food Supplement","authors":"Xinrui Yan, Yuan Tian, Kaibiao Sun","doi":"10.1002/mma.10805","DOIUrl":"https://doi.org/10.1002/mma.10805","url":null,"abstract":"<div>\u0000 \u0000 <p>Fish resources are indispensable natural resources for human beings. The 2020 report of FAO emphasized the critical need for sustainable development of fishery resources and effective resource management strategies. This study aims to investigate the exploitation of fishery resources from theoretical aspect. Firstly, a fishery prey–predator model involving cooperative hunting, fear effect, and additional food supplement is proposed. The impact of the triple effects on the population dynamics is deduced. Secondly, in order to meet human needs, rationally develop fishery resources, and maximize economic benefits, a weighted threshold feedback fishing strategy is adopted, and the complex dynamic behaviors induced by the weighted fishing strategies are discussed, including the existence and stability of the boundary periodic solution and the interior order-\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$$ k $$</annotation>\u0000 </semantics></math> periodic solutions. Finally, computer simulations are presented step by step to illustrate the theoretical results. The results provide a theoretical reference for scientific planning on exploitation and sustainable development of fishery resources.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9389-9403"},"PeriodicalIF":2.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949854","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

Stationary Distribution and Probability Density for a Stochastic Crime Model 随机犯罪模型的平稳分布和概率密度

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10809

Yanling Wu, Guangying Lv

引用次数: 0

Global Dynamics of a Stage Structure Prey–Predator Model With Fear, Group Defense, and Antipredator Behavior 具有恐惧、群体防御和反捕食行为的阶段结构捕食模型的全局动力学

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10845

Reshma K P, Ankit Kumar

{"title":"Global Dynamics of a Stage Structure Prey–Predator Model With Fear, Group Defense, and Antipredator Behavior","authors":"Reshma K P, Ankit Kumar","doi":"10.1002/mma.10845","DOIUrl":"https://doi.org/10.1002/mma.10845","url":null,"abstract":"<div>\u0000 \u0000 <p>This study proposes a 3-D stage-structured model, in which predator population is classified into immature and mature groups. The effect of mature predator's fear and the prey's antipredator behavior toward the juvenile predators are investigated. Furthermore, the effect of prey's collective defense in lowering the threat of predators is also examined. The investigation includes local stability analysis for existing steady-state solutions, revealing a number of global and local bifurcations such as homoclinic, transcritical, Hopf, and saddle-node bifurcations, as well as a codimension two Bogdanov–Takens bifurcation. We noticed that the tendency of prey to form groups causes the solutions to behave oscillatorily and that the level of fear eliminates these fluctuations and brings the system to a stable coexistence. The predator experiences a catastrophic fall when antipredator nature intensifies beyond a certain degree. The model also demonstrates bubbling phenomena in the maturation rate and the paradox of enrichment. To elucidate these bifurcations, we conduct biparametric analyses for various parameters, emphasizing their critical roles in predator survival and extinction. Numerical simulations and graphical illustrations validate our theoretical findings, demonstrating how fear, group defense, maturation rate, and counter attack behavior enrich the system dynamics.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9819-9839"},"PeriodicalIF":2.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949929","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

High Energy Blowup for a Class of Wave Equations With Critical Exponential Nonlinearity 一类具有临界指数非线性的波动方程的高能爆破

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10873

Tahir Boudjeriou, Ngo Tran Vu, Nguyen Van Thin

引用次数: 0

Stochastic Processes Described by Multidimensional Telegraph Equations 多维电报方程描述的随机过程

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10867

Anatoliy A. Pogorui, Ramón M. Rodríguez-Dagnino

引用次数: 0

An Efficient Numerical Approach for Solving Time-Space Fractional Wave Model of Multiterm Order Involving the Riesz Fractional Operators of Distributed Order With the Weakly Singular Kernel Along With Stability Analysis 具有弱奇异核分布阶Riesz分数算子的多项阶时-空分数波模型的有效数值求解方法及稳定性分析

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10860

Saeed Kosari, Mohammadhossein Derakhshan

{"title":"An Efficient Numerical Approach for Solving Time-Space Fractional Wave Model of Multiterm Order Involving the Riesz Fractional Operators of Distributed Order With the Weakly Singular Kernel Along With Stability Analysis","authors":"Saeed Kosari, Mohammadhossein Derakhshan","doi":"10.1002/mma.10860","DOIUrl":"https://doi.org/10.1002/mma.10860","url":null,"abstract":"<div>\u0000 \u0000 <p>In this manuscript, we propose an efficient numerical approach to solve the time-space fractional wave model of multiterm order, incorporating Riesz fractional operators of distributed order with a weakly singular kernel. The approach combines numerical techniques to approximate the model in both the spatial and temporal directions. For the time variable, the \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ L1 $$</annotation>\u0000 </semantics></math> approximation is employed, while a second-order accurate fractional-centered difference method is used for the spatial variable. We provide a detailed stability and convergence analysis for the fully discrete numerical scheme. To demonstrate the accuracy and efficiency of the proposed method, we present and simulate two numerical examples. The results of these examples are displayed graphically to illustrate the effectiveness of the approach.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9993-10007"},"PeriodicalIF":2.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949931","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

Extended Separation Method of Semi-Fixed Variables Together With Analytical Method for Solving Time Fractional Equation 半固定变量的扩展分离方法与求解时间分数阶方程的解析方法

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-03 DOI: 10.1002/mma.10856

Yinghui He, Weiguo Rui

{"title":"Extended Separation Method of Semi-Fixed Variables Together With Analytical Method for Solving Time Fractional Equation","authors":"Yinghui He, Weiguo Rui","doi":"10.1002/mma.10856","DOIUrl":"https://doi.org/10.1002/mma.10856","url":null,"abstract":"<div>\u0000 \u0000 <p>It is well known that investigation of exact solutions on nonlinear fractional partial differential equations (PDEs) is a very difficult work. In this paper, the separation method of semi-fixed variables is extended. Based on the original separation method, two kinds of new structures of the solutions in a hypothetical way are proposed. With the extended separation method of semi-fixed variables and the mapping method of Riccati equation combined, a new approach for searching exact solutions on time-fractional PDEs is introduced. To demonstrate the effect of the extended method, the time-fractional porous medium equation, time-fractional Hunter-Saxton equation, and time-fractional Fornberg-Whitham equation are solved under the Riemann-Liouville fractional differential operator. Different kinds of new exact solutions of the above three equations are obtained. In order to intuitively show the dynamic property of these exact solutions, the 3D-graphs of some solutions are illustrated as examples. Compared to the previous method, more abundant results can be obtained on solving some complex nonlinear time-fractional PDEs by use of this extended method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9934-9945"},"PeriodicalIF":2.1,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949932","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

Phase Portrait, Bifurcation and Chaotic Analysis, Variational Principle, Hamiltonian, Novel Solitary, and Periodic Wave Solutions of the New Extended Korteweg–de Vries–Type Equation 相位肖像，分岔和混沌分析，变分原理，哈密顿量，新扩展Korteweg-de vries型方程的新颖孤立波解和周期波解

IF 2.1 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2025-03-02 DOI: 10.1002/mma.10852

Kang-Jia Wang, Bo-Rong Zou, Hong-Wei Zhu, Shuai Li, Geng Li

{"title":"Phase Portrait, Bifurcation and Chaotic Analysis, Variational Principle, Hamiltonian, Novel Solitary, and Periodic Wave Solutions of the New Extended Korteweg–de Vries–Type Equation","authors":"Kang-Jia Wang, Bo-Rong Zou, Hong-Wei Zhu, Shuai Li, Geng Li","doi":"10.1002/mma.10852","DOIUrl":"https://doi.org/10.1002/mma.10852","url":null,"abstract":"<div>\u0000 \u0000 <p>The center task of this paper is to give the qualitative and quantitative investigations into the nonlinear dynamics of the new extended Korteweg–de Vries–type equation for shallow-water waves. Applying the traveling wave transformation and semi-inverse method (SIM), the variational principle (VP) is developed. Based on the VP, we extract the system's Hamiltonian. The planar dynamical system is then derived using the Galilean transformation, followed by phase portrait plotting and bifurcation analysis to explore the existence of different types of wave solutions. Meanwhile, the chaotic behaviors of the system are also analyzed by taking the external perturbation terms. Eventually, two robust approaches—the variational method that stemmed from the variational principle and Ritz method—along with the Hamiltonian-based method are employed to seek some wave solutions of the equation. Different kinds of the wave solutions like bell shape solitary, anti-bell shape solitary, and periodic wave solutions are obtained. The findings of this exploration are all novel and help us gain a deeper understanding of the nonlinear dynamics of the equation being studied.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9901-9909"},"PeriodicalIF":2.1,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950065","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