Communications in Nonlinear Science and Numerical Simulation最新文献_第2页

Convergence and superconvergence analysis for a mass conservative, energy stable and linearized BDF2 scheme of the Poisson–Nernst–Planck equations 泊松-纳斯特-普朗克方程的质量保守、能量稳定和线性化 BDF2 方案的收敛性和超收敛性分析

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-17 DOI: 10.1016/j.cnsns.2024.108351

{"title":"Convergence and superconvergence analysis for a mass conservative, energy stable and linearized BDF2 scheme of the Poisson–Nernst–Planck equations","authors":"","doi":"10.1016/j.cnsns.2024.108351","DOIUrl":"10.1016/j.cnsns.2024.108351","url":null,"abstract":"<div><div>In this paper, we consider a linearized BDF2 finite element scheme for the Poisson–Nernst–Planck (PNP) equations. By employing a novel approach, we rigorously derive unconditional optimal error estimates of the numerical solutions in the <span><math><mrow><msup><mrow><mi>l</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>l</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> norms, as well as superconvergent results. The key of the convergence and superconvergence analysis lies in deriving the stability of the finite element solutions in some stronger norms. The advantage of this approach is that there is no need to introduce a corresponding time discrete system, so it is more concise than the error split technique in previous literatures. Finally, we carry out two numerical examples to confirm the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319038","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

Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns 嵌入式循环模式对高维混沌吸引子的最小覆盖

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-16 DOI: 10.1016/j.cnsns.2024.108345

引用次数: 0

A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids 非牛顿流体中的非稳态热对流的分数时间步进方法

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-16 DOI: 10.1016/j.cnsns.2024.108350

{"title":"A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids","authors":"","doi":"10.1016/j.cnsns.2024.108350","DOIUrl":"10.1016/j.cnsns.2024.108350","url":null,"abstract":"<div><p>We propose a fractional-step method for the numerical solution of unsteady thermal convection in non-Newtonian fluids with temperature-dependent physical parameters. The proposed method is based on a viscosity-splitting approach, and it consists of four uncoupled steps where the convection and diffusion terms of both velocity and temperature solutions are uncoupled while a viscosity term is kept in the correction step at all times. This fractional-step method maintains the same boundary conditions imposed in the original problem for the corrected velocity solution, and it eliminates all inconsistencies related to boundary conditions for the treatment of the pressure solution. In addition, the method is unconditionally stable, and it allows the temperature to be transported by a non-divergence-free velocity field. In this case, we introduce a methodology to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>-order estimates for the pressure solution in their appropriate norms. Three numerical examples are presented to demonstrate the theoretical results and examine the performance of the proposed method for solving unsteady thermal convection in non-Newtonian fluids. The computational results obtained for the considered examples confirm the convergence, accuracy, and applicability of the proposed time fractional-step method for unsteady thermal convection in non-Newtonian fluids.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005355/pdfft?md5=e5d61a554d5c7b18eb6c8759401f1eac&pid=1-s2.0-S1007570424005355-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142244140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A stabilizer free weak Galerkin method with implicit θ-schemes for fourth order parabolic problems 四阶抛物问题的无稳定子弱 Galerkin 方法与隐式 θ 方案

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-16 DOI: 10.1016/j.cnsns.2024.108349

引用次数: 0

Evaluating the effects of nonlocality and numerical discretization in peridynamic solutions for quasi-static elasticity and fracture 评估准静态弹性和断裂的周动态解中的非局部性和数值离散化的影响

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-14 DOI: 10.1016/j.cnsns.2024.108343

{"title":"Evaluating the effects of nonlocality and numerical discretization in peridynamic solutions for quasi-static elasticity and fracture","authors":"","doi":"10.1016/j.cnsns.2024.108343","DOIUrl":"10.1016/j.cnsns.2024.108343","url":null,"abstract":"<div><p>The difference between the computational peridynamic results and the corresponding exact classical solutions is contributed by the error induced by numerical discretization and the nonlocality-induced difference. To evaluate and compare these contributions and investigate their dependence on the peridynamic influence functions, in this paper, we apply different peridynamic influence functions and different horizon factors (<em>m</em>, the ratio between the horizon size and the grid spacing) to conduct static (or quasi-static) tensile numerical tests. We calculate the difference between the peridynamic solutions and the corresponding classical solutions for static uniaxial tension of thin plates with or without hole, the J-integral of a single crack under Mode I loading condition, and the quasi-static fracture in a perforated thin plate. For the case of uniaxial tension in a thin, homogeneous plate, we separate the effects of nonlocality and numerical discretization by implementing the boundary conditions in different ways. The numerical results show that both the effects of nonlocality and numerical discretization correspond to the nonlocal constants of the influence functions (with few exceptions). For problems with the presence of the peridynamic surface effect, such as holes, influence function with weaker nonlocality is a better choice to obtain more accurate results.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005288/pdfft?md5=f06dcd4667bf45c3929df41f846aaeb3&pid=1-s2.0-S1007570424005288-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142270243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamics of a nonlinear infection viral propagation model with one fixed boundary and one free boundary 具有一个固定边界和一个自由边界的非线性感染病毒传播模型的动力学特性

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-13 DOI: 10.1016/j.cnsns.2024.108348

{"title":"Dynamics of a nonlinear infection viral propagation model with one fixed boundary and one free boundary","authors":"","doi":"10.1016/j.cnsns.2024.108348","DOIUrl":"10.1016/j.cnsns.2024.108348","url":null,"abstract":"<div><p>In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always expands to the half line <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span>, and that the virus and infected cells always die out when the <em>Basic Reproduction Number</em> <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, while the virus and infected cells have persistence properties when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. To obtain the persistence properties of virus and infected cells when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>, the most work of this paper focuses on the existence and uniqueness of bounded positive equilibrium solutions for subsystems and the existence of positive equilibrium solutions for the entire system.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005331/pdfft?md5=b3fa42804adbee714122d52eb5b046ee&pid=1-s2.0-S1007570424005331-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142232237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Event-triggered impulsive control for nonlinear stochastic delayed systems and complex networks 非线性随机延迟系统和复杂网络的事件触发脉冲控制

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-12 DOI: 10.1016/j.cnsns.2024.108305

{"title":"Event-triggered impulsive control for nonlinear stochastic delayed systems and complex networks","authors":"","doi":"10.1016/j.cnsns.2024.108305","DOIUrl":"10.1016/j.cnsns.2024.108305","url":null,"abstract":"<div><p>In this paper, we probe the <span><math><mi>p</mi></math></span>th moment exponential stability (<span><math><mrow><mi>p</mi><mo>−</mo></mrow></math></span>ES) of stochastic delayed systems subject to event-triggered delayed impulsive control (ETDIC), where the impulsive intensities are assumed to be positive random variables. Based on event-triggered mechanism (ETM) in the sense of expectation, some new sufficient conditions are developed to ensure the stability of the addressed system with Zeno-free behavior. The Lyapunov–Razumikhin method is adopted to handle the time-varying delay in continuous dynamics, and the concept of average random impulsive estimation (ARIE) is introduced to reduce the design requirements of the controller. Especially, the proposed ETDIC strategy not only generates the impulse time sequence according to the predesigned ETM, but also removes the limitations on the size of time delays. Furthermore, the ETM serves as a solution for synchronization problems in complex neural networks. Finally, two examples are given to illustrate the effectiveness of our conclusions.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424004908/pdfft?md5=702bc9c8fadf9ab3bd653778d3c4cfef&pid=1-s2.0-S1007570424004908-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142232236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Graph-let based approach to evolutionary behaviors in chaotic time series 基于子图的混沌时间序列演化行为方法

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-11 DOI: 10.1016/j.cnsns.2024.108344

{"title":"Graph-let based approach to evolutionary behaviors in chaotic time series","authors":"","doi":"10.1016/j.cnsns.2024.108344","DOIUrl":"10.1016/j.cnsns.2024.108344","url":null,"abstract":"<div><p>In the Graph-let based time series analysis, a time series is mapped into a series of graph-lets, representing the local states respectively. The bridges between successive graph-lets are reduced simply to a linkage with an information of occurrence. In the present work, we focus our attention on the bridge series, i.e., preserve the structures of the bridges and reduce the states into nodes. The bridge series can tell us how the system evolves. Technically, the ordinal partition algorithm is adopted to construct the graph-lets and the bridges. Results for the Logistic Map, the Hénon Map, and the Lorenz System show that the statistical properties for transition frequency network for the bridges, e.g., the number of visited bridges and the average out-entropy-degree, have the capability of characterizing chaotic processes, being equivalent with the Lyapunov exponent. What is more, the topological structure can display the details of the contributions of the transitions between the bridges to the statistical properties.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S100757042400529X/pdfft?md5=3e20263aeff45276fee75ec9fb3474b9&pid=1-s2.0-S100757042400529X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global well-posedness of strong solutions to the two-dimensional inhomogeneous biaxial nematic liquid crystal flow with vacuum 带真空的二维非均质双轴向列液晶流动强解的全局拟合性

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-11 DOI: 10.1016/j.cnsns.2024.108334

引用次数: 0

Dynamical behaviors in perturbative longitudinal vibration of microresonators under the parallel-plate electrostatic force 平行板静电力下微谐振器扰动纵向振动的动力学行为

IF 3.4 2区数学

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-10 DOI: 10.1016/j.cnsns.2024.108341

{"title":"Dynamical behaviors in perturbative longitudinal vibration of microresonators under the parallel-plate electrostatic force","authors":"","doi":"10.1016/j.cnsns.2024.108341","DOIUrl":"10.1016/j.cnsns.2024.108341","url":null,"abstract":"<div><p>The dynamic model for perturbative longitudinal vibration of microresonators subjected to the parallel-plate electrostatic force, which can be converted into a cubic oscillator with nonlinear polynomials, is established in this manuscript. The orbits and global dynamical behaviors of the cubic oscillator at full state are studied both analytically and numerically. The expressions of homoclinic orbits and subharmonic orbits are obtained analytically by solving the Hamilton system. The scenarios of phase portraits and equilibria are given. With the Melnikov method, the critical value of chaos arising from homoclinic intersections is derived analytically. The investigation yields intriguing dynamical phenomena, including the controllable frequencies that regulate the system without inducing chaos. The conditions for the occurrence of subharmonic bifurcations of integer order are presented with the subharmonic Melnikov method. Besides, the results indicate that the system does not undergo fractional order subharmonic bifurcation and it can reach a chaotic state through a finite number of integer order subharmonic bifurcations. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré cross-sections, Lyapunov exponential spectrums and basins of attractor are given, which are consistent with theoretical results.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424005264/pdfft?md5=6f80ec23ddf4f3580ecc87bdc48abd82&pid=1-s2.0-S1007570424005264-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142169555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0