Journal of Computational and Applied Mathematics最新文献_第2页

A novel multilevel finite element method for a generalized nonlinear Schrödinger equation 广义非线性薛定谔方程的新型多级有限元方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116280

{"title":"A novel multilevel finite element method for a generalized nonlinear Schrödinger equation","authors":"","doi":"10.1016/j.cam.2024.116280","DOIUrl":"10.1016/j.cam.2024.116280","url":null,"abstract":"<div><p>In this article, we focus on an efficient multilevel finite element method to solve the time-dependent nonlinear Schrödinger equation which is one of the most important equations of mathematical physics. For the time derivative, we adopt implicit schemes including the backward Euler method and the Crank–Nicolson method. Based on these stable implicit schemes, the proposed method requires solving a nonlinear elliptic problem at each time step. For these nonlinear elliptic equations, a multilevel mesh sequence is constructed. At each mesh level, we first derive a rough approximation by correcting the approximation of the previous mesh level in a special correction subspace. The correction subspace is composed of a coarse finite element space and an additional approximate solution derived from the previous mesh level. Next, we only need to solve a linearized elliptic equation by inserting the rough approximation into the nonlinear term. Then, we derive an accurate approximate solution by performing the aforementioned solving process on the multilevel mesh sequence until we reach the final mesh level. Owing to the special construct of the correction subspace, we derive a multilevel finite element method to solve the nonlinear Schrödinger equation for the first time, and meanwhile we also derive an optimal error estimate with linear computational complexity. Additionally, unlike the existing multilevel methods for nonlinear problems, that typically require bounded second-order derivatives of the nonlinear terms, the nonlinear term in our study requires only one-order derivatives. Numerical results are provided to support our theoretical analysis and demonstrate the efficiency of the presented method.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173521","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 analysis and applicability of a domain decomposition method with nonlocal interface boundary conditions 具有非局部界面边界条件的域分解方法的收敛性分析和适用性

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116276

{"title":"Convergence analysis and applicability of a domain decomposition method with nonlocal interface boundary conditions","authors":"","doi":"10.1016/j.cam.2024.116276","DOIUrl":"10.1016/j.cam.2024.116276","url":null,"abstract":"<div><p>In the past, the domain decomposition method was developed successfully for solving large-scale linear systems. However, the problems with significant nonlocal effect remain a major challenger for applying the method efficiently. In order to sort out the problem, a non-overlapping domain decomposition method with nonlocal interface boundary conditions was recently proposed and studied both theoretically and numerically. This paper is the report on the further development of the method, aiming to provide a comprehensive convergence analysis of the method, with supplementary numerical tests to support the theoretical result. The nonlocal effect of the problem is found to be reflected in both the governing equation and boundary conditions, and the effect of the latter was never taken into account, although playing a significant role in affecting the convergence. In addition, the paper extends the applicability of the analysis result drawn from the Poisson’s equation to more complicated problems by examining the symbols of the Steklov–Poincaré operators. The extended application includes a model equation arising from fluid dynamics and the high performance of the domain decomposition method in solving this equation is better elaborated.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241450","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

Mixed finite element method for multi-layer elastic contact systems 多层弹性接触系统的混合有限元法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116281

引用次数: 0

A discrete fractional order cournot duopoly game model with relative profit delegation: Stability, bifurcation, chaos, 0-1 testing and control 具有相对利润委托的离散分数阶库诺二元垄断博弈模型：稳定性、分岔、混沌、0-1 检验和控制

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116284

引用次数: 0

A penalty method for approximation of the stationary Stokes–Darcy problem 近似静止斯托克斯-达西问题的惩罚法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-12 DOI: 10.1016/j.cam.2024.116272

引用次数: 0

Stability of open-loop Nash equilibria for n-person nonzero-sum bounded rationality generalized differential games n人非零和有界理性广义微分博弈开环纳什均衡的稳定性

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-11 DOI: 10.1016/j.cam.2024.116260

{"title":"Stability of open-loop Nash equilibria for n-person nonzero-sum bounded rationality generalized differential games","authors":"","doi":"10.1016/j.cam.2024.116260","DOIUrl":"10.1016/j.cam.2024.116260","url":null,"abstract":"<div><p>The problem of determining the existence of Nash equilibria in <span><math><mi>n</mi></math></span>-person nonzero-sum generalized differential games is highly intricate and constrained by the advancement of partial differential equations theory. There is limited existing research literature on this subject. This paper presents an existence theorem for open-loop Nash equilibria employing the Fan-Glicksberg fixed point theorem. The <span><math><mi>n</mi></math></span>-person nonzero-sum bounded rationality generalized differential game model is formulated by introducing a bounded rationality function, and its structural stability and robustness are studied. The conclusions indicate that in the sense of Baire classification, most <span><math><mi>n</mi></math></span>-person nonzero-sum bounded rationality generalized differential games are structurally stable and robust in the set of <span><math><mi>ɛ</mi></math></span>-open-loop Nash equilibria, and we can approximate the equilibrium set obtained with full rationality generalized differential games by the <span><math><msup><mrow><mi>ɛ</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>-open-loop Nash equilibria set obtained with bounded rationality generalized differential games.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142241452","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

Alpha-robust mean–variance reinsurance and investment strategies with transaction costs 有交易成本的阿尔法稳健均值方差再保险和投资策略

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-11 DOI: 10.1016/j.cam.2024.116257

引用次数: 0

A refined first-order expansion formula in Rn: Application to interpolation and finite element error estimates Rn 中的精炼一阶扩展公式：应用于插值和有限元误差估计

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-10 DOI: 10.1016/j.cam.2024.116274

引用次数: 0

Positivity preserving and unconditionally stable numerical scheme for the three-dimensional modified Fisher–Kolmogorov–Petrovsky–Piskunov equation 三维修正 Fisher-Kolmogorov-Petrovsky-Piskunov 方程的正性保持和无条件稳定数值方案

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-10 DOI: 10.1016/j.cam.2024.116273

引用次数: 0

A fractional derivative model of the dynamic of dengue transmission based on seasonal factors in Thailand 基于季节因素的泰国登革热传播动态分数导数模型

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2024-09-07 DOI: 10.1016/j.cam.2024.116256

{"title":"A fractional derivative model of the dynamic of dengue transmission based on seasonal factors in Thailand","authors":"","doi":"10.1016/j.cam.2024.116256","DOIUrl":"10.1016/j.cam.2024.116256","url":null,"abstract":"<div><p>Climate variability affects the changes in controlling diseases transferred by insects. An increase in the population, the growth of communities, and a lack of public health infrastructure bring about the return of diseases of which insects are carriers, one of the illness issues. Therefore, the disease control is significant to help reduce the burden on the government and strengthen the country's public health structure. This research proposes a novel approach to modeling dengue fever dynamics, we employ a fractional derivative model with the Atangana–Baleanu–Caputo derivative, which offers a more accurate representation of real-world disease dynamics compared to traditional integer-order models. Basic qualifications are proposed. Equilibrium points and basic reproduction numbers are analyzed. The next-generation matrix method is used to identify the transmission. Besides, parameter sensitivity analysis is performed to learn about factors affecting input parameter values' effects on the basic reproduction number. It was found that the most common parameter affecting the transmission was the biting rate of mosquitoes was 1. In addition, the existence and uniqueness of the solution are examined using the Banach fixed point theorem. The Toufik–Atangana method is used for the numerical examination of a fractional version of the proposed model. We compared different values of fractional-order α=0.965, 0.975, 0.985, 0.995 and 1 it was found that when the order of derivatives decreases, the transmission shall decrease accordingly. This research provides valuable insights for developing effective control strategies to reduce the burden of dengue fever and strengthen public health systems.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229280","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