Applied Mathematics and Computation最新文献

{"title":"Natural extension of a Lie algebra A4,18b,|b|≤1, realizations, invariant systems and integrability","authors":"Muhammad Ayub , Saira Bano","doi":"10.1016/j.amc.2025.129274","DOIUrl":"10.1016/j.amc.2025.129274","url":null,"abstract":"<div><div>In the frame of Lie theory, the classical successive reduction of order for scalar ODEs is not much effective for system of differential equations due to technical hurdles. Lie algebraic approach is utilized to overcome these hurdles, then further invoked for the classification, linearization and integrability of system of differential equations. But in the case of higher dimension, this approach has also its own limitations due to classification of low dimensional Lie algebras and corresponding realizations. In the realm of Lie algebra theory, a natural extension refers to the process that involves enlarging a Lie algebra by adding new elements or structures while maintaining the fundamental algebraic properties. This extension technique finds applications in various fields, including physics, geometry, and mathematics.</div><div>In this paper, retaining <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>18</mn></mrow><mrow><mi>b</mi><mo>,</mo><mi>N</mi></mrow></msubsup><mo>,</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></span> as a base algebra in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>)</mo></math></span>-dimensional space, examined in <span><span>[2]</span></span>, a possible natural extension of underlying Lie algebra is investigated and also constructed associated realizations. Lie algebraic approach with natural extension is utilized for the analysis of a system of <em>n</em> second-order ODEs possessing extended form of Lie algebra <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>18</mn></mrow><mrow><mi>b</mi><mo>,</mo><mi>N</mi></mrow></msubsup><mo>,</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></span> in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>)</mo></math></span>-dimensional space to <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>n</mi><mo>)</mo></math></span>-dimensional space. In this research work, the extension of underlying Lie algebra, corresponding realizations and canonical forms associated with systems under consideration, have been formulated. Moreover, the integrability of investigated canonical forms for system of <em>n</em> second-order ODEs affiliated with extended form of Lie algebra <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>18</mn></mrow><mrow><mi>b</mi><mo>,</mo><mi>N</mi></mrow></msubsup><mo>,</mo><mo>|</mo><mi>b</mi><mo>|</mo><mo>≤</mo><mn>1</mn></math></span> in <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>)</mo></math></span>-dimensional space to <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>n</mi><mo>)</mo></math></span>-dimensional space is described and three integrable classes of underlying systems have been deduced. In addition, two new classes of algebraic linearization criteria for a system of <em>n</em> second-order ODEs admitting Lie algebra <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>,</mo><mn>18</mn></mrow><mrow>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129274"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990369","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":"New stabilized mixed finite element methods for two-field poroelasticity with low permeability","authors":"Linshuang He,&nbsp;Luru Jing,&nbsp;Minfu Feng","doi":"10.1016/j.amc.2025.129285","DOIUrl":"10.1016/j.amc.2025.129285","url":null,"abstract":"<div><div>In this paper, we develop new stabilized mixed finite element (MFE) methods for two-field Biot's model of poroelasticity. We employ the H(div)-conforming element and discontinuous element to approximate the displacement and pressure variables, and use the <em>θ</em>-scheme to discretize time. By adding the stabilization term based on polynomial pressure projection, the fully-discrete and stabilized MFE methods are obtained. Our methods work well for both inf-sup stable and unstable element pairs, and provide oscillation-free pressure solutions in heterogeneous materials with low-permeable layers or interfaces. These methods are also volumetric locking-free and locally mass-conservative. We establish optimal <em>a priori</em> error estimates and perform numerical examples, which show the uniform robustness of the proposed methods for low permeability.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129285"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990280","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":"Convergence analysis of an efficient multistep pseudo-spectral continuous Galerkin approach for solving Volterra integro-differential equations","authors":"Yin Yang ,&nbsp;Pai Yao ,&nbsp;Emran Tohidi","doi":"10.1016/j.amc.2025.129284","DOIUrl":"10.1016/j.amc.2025.129284","url":null,"abstract":"<div><div>In this research article, we apply the multistep pseudo-spectral continuous Galerkin approach for solving the first-order Volterra integro-differential equations by the aid of the orthogonal Legendre polynomials. This approach is a recursive scheme that the accuracy of the numerical solution at the present subinterval depends on the numerical solutions at the previous subintervals. Convergence analysis of the suggested numerical approach is discussed via using an important auxiliary problem. Extensive numerical test problems with high oscillating analytical solutions, exact solutions with steep gradients, and long time computational intervals are considered and both of the h-version and p-version convergence rates are examined experimentally. Finally, the conclusions regarding the presented approach and the considered model are provided and we point out to some other models that can be solved numerically via this efficient and robust method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129284"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990368","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 composite filter-based approach to adaptive prescribed-time output-feedback control of strict-feedback nonlinear systems with output and input quantization","authors":"Chen Chen,&nbsp;Jinghao Li","doi":"10.1016/j.amc.2025.129279","DOIUrl":"10.1016/j.amc.2025.129279","url":null,"abstract":"<div><div>This paper investigates the adaptive prescribed-time control problems of strict-feedback nonlinear systems with output quantization, input quantization and unknown control coefficients. Firstly, a quantized K-filter is constructed to estimate the system states. Then, a set of command filters are introduced to smooth the discontinuous stabilizing functions and reduce the computational burden. Moreover, a class of scaling functions are designed to achieve the desired prescribed-time tracking performance. Based on the quantized K-filter, a set of command filters and a class of scaling functions, a set of new error variables are established to facilitate the design of the quantized composite filter-based adaptive prescribed-time control method. It is proved that the tracking error converges to an adjustable compact set within a prescribed time. Finally, two examples are provided to illustrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129279"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990367","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":"Data-driven bipartite synchronization control of multi-agent systems with asymmetric input saturation over switching networks","authors":"Ziwen Shen ,&nbsp;Tao Dong ,&nbsp;Tingwen Huang","doi":"10.1016/j.amc.2025.129280","DOIUrl":"10.1016/j.amc.2025.129280","url":null,"abstract":"<div><div>This paper addresses the bipartite synchronization (BS) issue of nonlinear discrete-time multi-agent systems (NDTMASs) with asymmetric input saturation in switching cooperative-competitive networks. First, a local neighborhood error system (LNES) is constructed based on the switching cooperative-competitive networks. By utilizing a hyperbolic function, we design a novel local cost function and derive an optimal control policy. Based on this control policy, we construct a novel saturation-input policy iteration (SIPI) technique. Furthermore, we establish the convergence of the SIPI algorithm. It is demonstrated that the LNES can converge to zero, and thus the BS problem for MASs can be solved. To implement the SIPI algorithm, a control framework based on an actor-critic architecture is constructed. To achieve asymmetric input saturation, we select an asymmetric constrained function as the activation function for the actor network. Finally, an example is presented to illustrate the reliability of our approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129280"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990366","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":"Stochastic stability of networked control systems with packet disordering via a gain-scheduling controller","authors":"Huihui Ji ,&nbsp;Shengyuan Xu ,&nbsp;He Zhang ,&nbsp;Chenlong Li ,&nbsp;Yuhua Xu","doi":"10.1016/j.amc.2025.129282","DOIUrl":"10.1016/j.amc.2025.129282","url":null,"abstract":"<div><div>It is addressed the problem of almost sure stability for networked control systems (NCSs), where the order of the control signal is possible to be disordering over a communication network. A stochastic configuration network algorithm is employed to record and predict the packet order, which is random to allot input biases or weights and evaluates the output wights. Under the algorithm, a stochastic parameter appears in the controlled system and is assumed to obey a Markov distribution. In this paper, a group of scheduling controllers in a controlled interval are chosen subjected to an underlying Markov chain and the execution time allotted to the controller is subjected to a hidden stochastic process. Thus, the NCSs based on stochastic scheduling include complex random variables. Combining Lyapunov analysis method and some stochastic analysis tools, almost sure stability conditions are given. Finally, the obtained results are applied into addressing the problem of stochastic scheduling control of a quadruple-tank process.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129282"},"PeriodicalIF":3.5,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990365","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":"Leveraging surrounding past strategies to maintain cooperation in the perverse prisoner's dilemma","authors":"Akihiro Takahara ,&nbsp;Tomoko Sakiyama","doi":"10.1016/j.amc.2024.129272","DOIUrl":"10.1016/j.amc.2024.129272","url":null,"abstract":"<div><div>In spatial game theory, developed models preserving cooperators often incorporate memory to enhance realism. This study examined the role of memory in a spatial prisoner's dilemma. In the proposed model, all players use their own and their neighbors’ past memories and current states to update strategies under specific conditions. When a player's score is lower than that of a neighbor using the same strategy, and that neighbor has the highest score among all neighbors, the player revisits past strategies and adopts a less experienced strategy. This rule adjusts behavior under unfavorable conditions. Results showed that the proposed model effectively retains cooperators. Previous studies have often necessitated the use of long-term memory and intricate systems; however, the present model eliminates these requirements. Instead, it sustains cooperation by employing a strategy that relies on minimal historical information when determining the subsequent course of action.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129272"},"PeriodicalIF":3.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968138","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":"Controllability of piecewise linear state-delay systems","authors":"Huiping Luo ,&nbsp;JinRong Wang","doi":"10.1016/j.amc.2025.129281","DOIUrl":"10.1016/j.amc.2025.129281","url":null,"abstract":"<div><div>In this paper, we study the controllability of piecewise linear state-delay systems (PLSDSs). To do this, we introduce a series of new functions and give the explicit representation of the solution. Then, the Gramian and the rank criteria for the controllability of PLSDSs are established by the piecewise delayed Gramian matrix. Further, all control functions driving the solution from an initial function to a desired final state are characterized by virtue of shifted Legendre polynomials. In addition, the controllability of PLSDSs constrained in an invariant subspace and weakly nonlinear piecewise systems are discussed as well, respectively. Numerical examples are provided to verify the effectiveness of theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129281"},"PeriodicalIF":3.5,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968137","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":"An algebraic algorithm for the total least squares problem in commutative quaternionic theory","authors":"Tongsong Jiang ,&nbsp;Dong Zhang ,&nbsp;Zhenwei Guo ,&nbsp;V.I. Vasil'ev","doi":"10.1016/j.amc.2024.129268","DOIUrl":"10.1016/j.amc.2024.129268","url":null,"abstract":"<div><div>A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations <span><math><mi>A</mi><mi>X</mi><mo>≈</mo><mi>B</mi></math></span> with errors in the matrices <em>A</em> and <em>B</em>. In the theoretical studies and numerical calculations of commutative quaternionic theory, the CQTLS problem is an extremely effective tool for the study of telecommunications, geodesy, and image processing theory. This paper, by means of the real representation of a commutative quaternion matrix, studies the CQTLS problem, derives necessary and sufficient conditions for the CQTLS problem has a commutative quaternion solution, and gives an algebraic algorithm for solving the CQTLS problem.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129268"},"PeriodicalIF":3.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968140","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 learning-based sliding mode control for switching systems with dead zone","authors":"Bo Wang ,&nbsp;Fucheng Zou ,&nbsp;Junhui Wu ,&nbsp;Jun Cheng","doi":"10.1016/j.amc.2025.129283","DOIUrl":"10.1016/j.amc.2025.129283","url":null,"abstract":"<div><div>This paper focuses on the problem of adaptive neural network sliding mode control for switching systems affected by dead zones. Distinct from existing rules defined by transition and sojourn probabilities, a broader switching rule is proposed based on duration-time-dependent sojourn probabilities. A neural network strategy for compensation is implemented to mitigate the effects of the dead zone. Moreover, a sliding mode control law incorporating a learning term is designed, effectively reducing chattering compared to conventional sliding mode control. Employing a stochastic Lyapunov function grounded in the joint distribution of duration time and system mode, sufficient criteria for designing the adaptive neural network-based controller are established. Finally, the effectiveness of the proposed method is demonstrated through two simulated examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129283"},"PeriodicalIF":3.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968139","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}