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

Convex combinations of some convergent sequences 某些收敛序列的凸面组合

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-02 DOI: 10.1002/mma.10463

Stevo Stević

引用次数: 0

Nonexistence of solutions to quasilinear Schrödinger equations with a parameter 带参数的准线性薛定谔方程解的不存在性

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-02 DOI: 10.1002/mma.10452

Hongwang Yu, Yunfeng Wei, Caisheng Chen, Qiang Chen

引用次数: 0

Spectral methods utilizing generalized Bernstein‐like basis functions for time‐fractional advection–diffusion equations 利用广义伯恩斯坦基函数的分时平流扩散方程谱方法

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-02 DOI: 10.1002/mma.10390

Shahad Adil Taher Algazaa, Jamshid Saeidian

{"title":"Spectral methods utilizing generalized Bernstein‐like basis functions for time‐fractional advection–diffusion equations","authors":"Shahad Adil Taher Algazaa, Jamshid Saeidian","doi":"10.1002/mma.10390","DOIUrl":"https://doi.org/10.1002/mma.10390","url":null,"abstract":"This paper presents two methods for solving two‐dimensional linear and nonlinear time‐fractional advection–diffusion equations with Caputo fractional derivatives. To effectively manage endpoint singularities, we propose an advanced space‐time Galerkin technique and a collocation spectral method, both employing generalized Bernstein‐like basis functions (GBFs). The properties and behaviors of these functions are examined, highlighting their practical applications. The space‐time spectral methods incorporate GBFs in the temporal domain and classical Bernstein polynomials in the spatial domain. Fractional equations frequently produce irregular solutions despite smooth input data due to their singular kernel. To address this, GBFs are applied to the time derivative and classical Bernstein polynomials to the spatial derivative. A thorough error analysis confirms the technique's accuracy and convergence, offering a robust theoretical basis. Numerical experiments validate the method, demonstrating its effectiveness in solving both linear and nonlinear time‐fractional advection–diffusion equations.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220045","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

Wave propagation for the isentropic compressible Navier–Stokes/Allen–Cahn system 等熵可压缩 Navier-Stokes/Allen-Cahn 系统的波传播

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-02 DOI: 10.1002/mma.10458

Yazhou Chen, Houzhi Tang, Yue Zhang

引用次数: 0

Global solution of spherically symmetric compressible Navier–Stokes equations with bounded density and density‐dependent viscosity 密度和粘度受限的球面对称可压缩纳维-斯托克斯方程的全局解法

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10433

Xueyao Zhang

引用次数: 0

Spectral properties for discontinuous Dirac system with eigenparameter‐dependent boundary condition 具有特征参数相关边界条件的不连续狄拉克系统的频谱特性

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10364

Jiajia Zheng, Kun Li, Zhaowen Zheng

引用次数: 0

Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi‐term differential equations 不同阶的卡普托分数导数和黎曼-刘维尔积分及其在多期微分方程中的应用研究

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10392

Ghaus Ur Rahman, Dildar Ahmad, José Francisco Gómez‐Aguilar, Ravi P. Agarwal, Amjad Ali

{"title":"Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi‐term differential equations","authors":"Ghaus Ur Rahman, Dildar Ahmad, José Francisco Gómez‐Aguilar, Ravi P. Agarwal, Amjad Ali","doi":"10.1002/mma.10392","DOIUrl":"https://doi.org/10.1002/mma.10392","url":null,"abstract":"In this article, we initially provided the relationship between the RL fractional integral and the Caputo fractional derivative of different orders. Additionally, it is clear from the literature that studies into boundary value problems involving multi‐term operators have been conducted recently, and the aforementioned idea is used in the formulation of several novel models. We offer a unique coupled system of fractional delay differential equations with proper respect for the role that multi‐term operators play in the research of fractional differential equations, taking into account the newly established solution for fractional integral and derivative. We also made the assumptions that connected integral boundary conditions would be added on top of ‐fractional differential derivatives. The requirements for the existence and uniqueness of solutions are also developed using fixed‐point theorems. While analyzing various sorts of Ulam's stability results, the qualitative elements of the underlying model will also be examined. In the paper's final section, an example is given for purposes of demonstration.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220047","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

The analysis of traveling wave structures and chaos of the cubic–quartic perturbed Biswas–Milovic equation with Kudryashov's nonlinear form and two generalized nonlocal laws 带有库德亚绍夫非线性形式和两个广义非局部定律的立方-方波扰动比斯瓦斯-米洛维奇方程的行波结构和混沌分析

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10462

Shuang Li, Xing‐Hua Du

{"title":"The analysis of traveling wave structures and chaos of the cubic–quartic perturbed Biswas–Milovic equation with Kudryashov's nonlinear form and two generalized nonlocal laws","authors":"Shuang Li, Xing‐Hua Du","doi":"10.1002/mma.10462","DOIUrl":"https://doi.org/10.1002/mma.10462","url":null,"abstract":"The cubic–quartic perturbed Biswas–Milovic equation, which contains Kudryashov's nonlinear form and two generalized nonlocal laws, has been explored qualitatively and quantitatively, as demonstrated in the present work. The research methods used include the complete discrimination system for polynomial method and the trial equation method. The results show that the Hamiltonian has the conservation property, and the global phase diagrams obtained via the bifurcation method reveal the existence of periodic and soliton solutions. Furthermore, we fully classify all the single traveling wave solutions to substantiate our findings, covering singular solutions, solitons, and Jacobian elliptic function solutions. We analyze their topological stabilities and present two‐dimensional graphs of solutions. We also delve deeper into the dynamic system by incorporating the perturbation item to explore the chaotic phenomena associated with the equation. These outcomes are valuable for studying the propagation of high‐order dispersive optical solitons and have potential applications in optimizing optical communication systems to improve efficiency.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220053","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

Instability of H1$$ {H}^1 $$‐stable periodic peakons for the Novikov equation 诺维科夫方程 H1$$ {H}^1 $$ 稳定周期峰子的不稳定性

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10436

Gezi Chong, Ying Fu, Hao Wang

引用次数: 0

A family of quadrature formulas with their error bounds for convex functions and applications 凸函数的一系列正交公式及其误差范围和应用

IF 2.9 3区数学

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-31 DOI: 10.1002/mma.10460

Muhammad Toseef, Abdul Mateen, Muhammad Aamir Ali, Zhiyue Zhang

引用次数: 0