Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Two-step inertial accelerated algorithms for solving split feasibility problem with multiple output sets","authors":"C.C. Okeke ,&nbsp;K.O. Okorie ,&nbsp;C.E. Nwakpa ,&nbsp;O.T. Mewomo","doi":"10.1016/j.cnsns.2024.108461","DOIUrl":"10.1016/j.cnsns.2024.108461","url":null,"abstract":"<div><div>In this paper, we present and study two new two-step inertial accelerated algorithms for finding an approximate solution of split feasibility problems with multiple output sets. Our methods are extensions of CQ algorithms previously studied in the literature. In contrast to the related iterative methods for solving SFP, our methods incorporate a two-step inertial technique that speeds up the convergence rate of the generated sequences to the unique solution of SFP studied in this work. Furthermore, we present weak and strong convergence results where the strong convergence result of our method is obtained without the on-line rule, a feature absent in related algorithms in the literature. Finally, we demonstrate the applicability and performance of our algorithms through numerical experiments. Our numerical results reveal that our methods perform better than existing related methods in the literature.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108461"},"PeriodicalIF":3.4,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720509","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}

{"title":"Navigating PINNs via maximum residual-based continuous distribution","authors":"Yanjie Wang ,&nbsp;Feng Liu ,&nbsp;Faguo Wu ,&nbsp;Xiao Zhang","doi":"10.1016/j.cnsns.2024.108460","DOIUrl":"10.1016/j.cnsns.2024.108460","url":null,"abstract":"<div><div>Physics-informed neural networks are a powerful deep-learning framework that integrates physical laws to solve partial differential equations, yet achieving fast convergence and high prediction accuracy remains challenging due to the ongoing issue of obtaining high-quality training data. In this study, we introduce a sampling-enhanced framework to unify residual-based sampling methods of PINNs. To address the limitations of existing adaptive sampling methods, we propose MRD (<strong>M</strong>aximum <strong>R</strong>esidual-based continuous <strong>D</strong>istribution) to navigate PINNs and move training points towards the high-residual region. It not only adopts a continuous form for more precise residual indication, but also effectively generates a high-quality training dataset. Our method is generic, straightforward, and easily extended to high-dimensional, dynamic and nonlinear PDEs. Experimental results across all five equations demonstrate a significant improvement in relative error, validating the generality and efficacy of our MRD method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108460"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746432","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}

{"title":"The time-fractional Allen–Cahn equation on geometric computational domains","authors":"Dongsun Lee ,&nbsp;Hyunju Kim","doi":"10.1016/j.cnsns.2024.108455","DOIUrl":"10.1016/j.cnsns.2024.108455","url":null,"abstract":"<div><div>Phase separation, the formation of two distinct phases from a single homogeneous mixture, has been extensively studied and observed in classical systems, typically as temperature changes. These separation phenomena depend on temperature and vary with different materials. We explore the numerical model, which shows various aspects of phase separation, such as time delay, the influence of heterogeneous materials on each domain, and the separation behavior in polyhedrons for industrial potentials.</div><div>This work investigates the time-fractional Allen–Cahn model with the Caputo fractional differential operator, which is particularly suited for capturing long waiting times in highly inhomogeneous porous media. We numerically examine the behavior of the order parameter <span><math><mi>u</mi></math></span> on the surfaces of polyhedral and conical computational domains. We achieve the numerical simulation using an explicit Predictor–Corrector method in conjunction with a collocation approach, where Non-Uniform Rational B-Spline (NURBS) geometrical mapping is applied. Through this numerical method, we simulate the behavior of the order parameter <span><math><mi>u</mi></math></span> on various surfaces of solids, investigating the effects of varying time-fractional derivative orders on each face of these geometries. We introduce the Schwarz alternating collocation method to handle discrepancies in boundary values when different time-fractional orders are applied to each subdomain.</div><div>Certain crystalline solids can be formed in materials science by joining different materials along their folding curves, resulting in varying material properties across boundaries. Observing phase separation in interconnected regions with varying material properties is challenging. Furthermore, phase separation that reflects the distinct characteristics of materials represented by time-fractional order differentiation in such interconnected regions with varying material properties has yet to be studied, making it a challenging problem, as far as our knowledge is concerned.</div><div>To address the aforementioned challenge, this study conducts a comprehensive series of numerical tests to investigate phase-field properties on surfaces of varying materials. Our thorough approach effectively captures how material properties are reflected across different geometries and how time-fractional behaviors vary on each surface. The numerical results illustrate critical phenomena, such as Ostwald ripening under varying time-fractional orders on the surface of geometries like cubes, tetrahedrons, prisms, and cones. Furthermore, we observe the curve shortening flow on the flattened sector of a circular conical domain, providing a complete picture of the behavior of the order parameter <span><math><mi>u</mi></math></span>.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108455"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720512","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}

{"title":"Resistance distances in stretched Cantor product networks","authors":"Jiaqi Fan ,&nbsp;Yuanyuan Li","doi":"10.1016/j.cnsns.2024.108458","DOIUrl":"10.1016/j.cnsns.2024.108458","url":null,"abstract":"<div><div>In this paper, we consider resistance distances in stretched Cantor product networks, a family of non-self-similar networks. By constructing the networks in a iterated way, we give an approach to encode every node in their vertex set. And then we simplify the complex resistor networks by induction on the basic network pattern. Using classical results of circuit theory, we obtain the exact formulae of the resistance distances of some pairs of nodes in stretched Cantor product networks.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108458"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679154","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}

{"title":"On a class of Schrödinger–Kirchhoff-double phase problems with convection term and variable exponents","authors":"Noureddine Moujane ,&nbsp;Mohamed El Ouaarabi","doi":"10.1016/j.cnsns.2024.108453","DOIUrl":"10.1016/j.cnsns.2024.108453","url":null,"abstract":"<div><div>In this paper, we investigate the existence of solutions for double-phase problems with variable exponents of the Kirchhoff–Schrödinger type, incorporating a convection term. By imposing certain assumptions and utilizing the topological degree for a class of <span><math><mrow><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></mrow></math></span>-demicontinuous operators, along with the Galerkin method within the framework of Musielak–Orlicz–Sobolev spaces, we establish the existence of strong generalized solutions and weak solutions for the problems under consideration.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108453"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679155","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}

{"title":"Fixed-time NN-based adaptive fault-tolerant control for heterogeneous vehicular platoon system with improved exponential spacing policy","authors":"Haonan Qi ,&nbsp;Liang Cao ,&nbsp;Hongru Ren ,&nbsp;Meng Zhao","doi":"10.1016/j.cnsns.2024.108454","DOIUrl":"10.1016/j.cnsns.2024.108454","url":null,"abstract":"<div><div>This paper is concerned with the distributed fixed-time neural network adaptive tracking control issue for heterogeneous vehicular platoon suffered from actuator faults. Due to the string instability of vehicles caused by non-zero initial spacing errors (ISEs), an improved exponential spacing policy is proposed to eliminate the influence of non-zero ISEs by introducing a compensated term, while guaranteeing the traffic flow stability. Subsequently, a fixed-time platoon control scheme is constructed, where the singularity problem caused by the negative exponent terms of controller is addressed by introducing a cosine-based scalar function. Moreover, the influence of actuator faults and uncertainties for vehicular platoon system is decreased with the control scheme, where the instability caused by maximum acceleration is avoided. The internal stability and string stability of the closed-loop system are proven through Lyapunov stability analysis. The simulation example and comparison results testify to the reliability of control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108454"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699696","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}

{"title":"The investigation of nonlinear dynamic characteristics of spur gear with angular misalignment error based on an improved dynamic model","authors":"Xiaoyu Che,&nbsp;Chao Zhang,&nbsp;Hu Yu,&nbsp;Rupeng Zhu","doi":"10.1016/j.cnsns.2024.108476","DOIUrl":"10.1016/j.cnsns.2024.108476","url":null,"abstract":"<div><div>Angular misalignment error is a prevalent occurrence in gear systems, mainly caused by manufacturing and installation errors in gearbox components. This significantly impacts the meshing characteristics of the system, making it necessary to carry out the nonlinear dynamic analysis of spur gear pairs with angular misalignment errors. In this study, a meshing stiffness model for a spur gear pair with angular misalignment error is established based on the Load Teeth Contact Analysis (LTCA) method. The effect of misalignment errors on the distribution of tooth surface stiffness are analyzed. Additionally, an improved dynamic model considering angular misalignment errors and variable backlash along the tooth width direction was proposed based on the lumped mass method and the slicing method. The effects of angular misalignment errors parallel and perpendicular to the meshing plane on the nonlinear dynamics of the system were studied. Frequency domain diagrams, Poincaré diagrams, and bifurcation diagrams were employed to comprehensively analyze the nonlinear characteristics of the system. The results indicate that with light loads, the system experiences a sequence of periodic and chaotic motions as <em>θ_a</em> increases, eventually returning to periodic motion. Conversely, <em>θ_v</em> shows minimal influence on the gear backlash, with the system exhibiting periodic motion when <em>θ_v</em> is small. As <em>θ_v</em> increases, the system transitions to chaotic motion before ultimately returning to periodic motion. Under heavy load conditions, as <em>θ_a</em> increases, the system transitions gradually from chaotic to periodic motion. However, regardless of the variations in <em>θ_v</em>, the system consistently remains in periodic motion.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108476"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698638","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}

{"title":"Consistency-enhanced modified SAV time-stepping method with relaxation for binary mixture of and viscous fluids","authors":"Jingwen Wu ,&nbsp;Zhijun Tan","doi":"10.1016/j.cnsns.2024.108451","DOIUrl":"10.1016/j.cnsns.2024.108451","url":null,"abstract":"<div><div>In this work, the binary mixture of nematic liquid crystals and viscous fluids (NLC-VF) system consists of the Cahn–Hilliard (CH) equations for the phase-field variable for the free interface, the Allen–Cahn (AC) type constitutive equation for the nematic director, and the incompressible Navier–Stokes (NS) equation for the two fluids. To address the computational challenges posed by this complex system, we propose a scheme that is fully decoupled, energy-stable and highly consistent, based on a modified scalar auxiliary variable (MSAV) with stabilization. Our approach employs two auxiliary variables: one derived from the nonlinear terms in the original energy, and the other leveraging the “zero-energy-contribution (ZEC) ”property satisfied by some nonlinear terms. To ensure consistency between the continuous and discrete auxiliary variables, we employ relaxation techniques. Besides, the proposed method enables sequential solving of each variable, and the computational overhead of the relaxation technique is minimal, resulting in highly efficient computation. We demonstrate the accuracy, stability, consistency, and practicality of the method through comprehensive numerical experiments, and provide rigorous proof of its unconditional energy stability.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108451"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699675","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}

{"title":"A representation-theoretical approach to higher-dimensional Lie–Hamilton systems: The symplectic Lie algebra sp(4,R)","authors":"Rutwig Campoamor-Stursberg ,&nbsp;Oscar Carballal ,&nbsp;Francisco J. Herranz","doi":"10.1016/j.cnsns.2024.108452","DOIUrl":"10.1016/j.cnsns.2024.108452","url":null,"abstract":"<div><div>A new procedure for the construction of higher-dimensional Lie–Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of intrinsic Lie–Hamilton system is defined, and a sufficiency criterion for this property given. Novel four-dimensional Lie–Hamilton systems arising from the fundamental representation of the symplectic Lie algebra <span><math><mrow><mi>s</mi><mi>p</mi><mrow><mo>(</mo><mn>4</mn><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> are obtained and proved to be intrinsic. Two distinguished subalgebras, the two-photon Lie algebra <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msub></math></span> and the Lorentz Lie algebra <span><math><mrow><mi>s</mi><mi>o</mi><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>, are also considered in detail. As applications, coupled time-dependent systems which generalize the Bateman oscillator and the one-dimensional Caldirola–Kanai models are constructed, as well as systems depending on a time-dependent electromagnetic field and generalized coupled oscillators. A superposition rule for these systems, exhibiting interesting symmetry properties, is obtained using the coalgebra method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108452"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698639","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}

{"title":"Stabilizer-free weak Galerkin method and its optimal L2 error estimates for the time-dependent Poisson—Nernst–Planck problem","authors":"Wenjuan Li ,&nbsp;Fuzheng Gao ,&nbsp;Xiaoming He","doi":"10.1016/j.cnsns.2024.108449","DOIUrl":"10.1016/j.cnsns.2024.108449","url":null,"abstract":"<div><div>This paper concerns a backward Euler stabilizer-free weak Galerkin finite element method (SFWG-FEM) for the time-dependent Poisson–Nernst–Planck (TD-PNP) problem. The scheme we propose utilizes spaces <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><msup><mrow><mrow><mo>[</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>j</mi></mrow></msub><mrow><mo>(</mo><mi>K</mi><mo>)</mo></mrow><mo>]</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span> to approximate the interior, edge, and discrete weak gradient spaces on each element <span><math><mi>K</mi></math></span> and edge <span><math><mrow><mi>e</mi><mo>⊂</mo><mi>∂</mi><mi>K</mi></mrow></math></span>, respectively. The proposed method is in a simple format similar to the regular finite element method, compatible with polygonal meshes, flexible in approximation function space, and unconditionally stable in time. Based on a rigorous analysis of a weak Galerkin Ritz projection error, which is derived by a dual problem, the superconvergence of the Ritz projection error estimates in energy norm results in optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> error estimates. Several numerical experiments are conducted to demonstrate our theoretical findings, where Oseen iteration is utilized for the nonlinear coupling terms.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108449"},"PeriodicalIF":3.4,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698637","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}