Mathematics and Computers in Simulation最新文献

{"title":"A high order numerical method for analysis and simulation of 2D semilinear Sobolev model on polygonal meshes","authors":"Ajeet Singh ,&nbsp;Hanz Martin Cheng ,&nbsp;Naresh Kumar ,&nbsp;Ram Jiwari","doi":"10.1016/j.matcom.2024.08.010","DOIUrl":"10.1016/j.matcom.2024.08.010","url":null,"abstract":"<div><p>In this article, we design and analyze a hybrid high-order method for a semilinear Sobolev model on polygonal meshes. The method offers distinct advantages over traditional approaches, demonstrating its capability to achieve higher-order accuracy while reducing the number of unknown coefficients. We derive error estimates for the semi-discrete formulation of the method. Subsequently, these convergence rates are employed in full discretization with the Crank–Nicolson scheme. The method is demonstrated to converge optimally with orders of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow></math></span> in the energy-type norm and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow></math></span> in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. The reported method is supported by a series of computational tests encompassing linear, semilinear and Allen–Cahn models.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006757","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":"Disturbance observer-based event-triggered impulsive control for nonlinear systems with unknown external disturbances","authors":"Ying Xing ,&nbsp;Xinyi He ,&nbsp;Xiaodi Li","doi":"10.1016/j.matcom.2024.08.012","DOIUrl":"10.1016/j.matcom.2024.08.012","url":null,"abstract":"<div><p>Input-to-state practical stability (<em>ISpS</em>) of a kind of nonlinear systems suffering from unknown exogenous disturbances is explored in this article, where a disturbance observer is established to estimate the information of the exogenous disturbances. To achieve <em>ISpS</em> of the system, the impulsive controller as well as state-feedback controller are both considered to regulate the discrete and continuous dynamics of the system, respectively. Especially, a novel disturbance observer-based event-triggered mechanism is devised to decide the release of impulsive control signal. Furthermore, several adequate conditions are given for excluding the occurrence of Zeno phenomenon. To confirm the feasibility of the proposed results, two numerical instances and their corresponding simulation results are presented.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006758","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":"Fractional order forestry resource conservation model featuring chaos control and simulations for toxin activity and human-caused fire through modified ABC operator","authors":"Muhammad Farman ,&nbsp;Khadija Jamil ,&nbsp;Changjin Xu ,&nbsp;Kottakkaran Sooppy Nisar ,&nbsp;Ayesha Amjad","doi":"10.1016/j.matcom.2024.07.038","DOIUrl":"10.1016/j.matcom.2024.07.038","url":null,"abstract":"<div><p>In this work, we proposed a nonlinear mathematical model with fractional-order differential equations employed to illustrate the impacts of depleted forestry resources with the effect of toxin activity and human-caused fire. The numerical and theoretical outcomes are based on the consideration of using a modified ABC-fractional-order depleted forestry resources dynamical system. In the theoretical aspect, we examination of solution positivity, existence, and uniqueness it makes use of Banach’s fixed point and the Leray Schauder nonlinear alternative theorem. The consecutive recursive sequences are purposefully designed to verify the existence of a solution to the depletion of forestry resources as delineated. To showcase the specificity and stability of the solution within the Hyers–Ulam framework, we employ the concepts and findings of functional analysis. Chaos control will stabilize the system following its equilibrium points by applying the regulate for linear responses technique. Using Lagrange polynomials insight of modified ABC-fractional-order, we conduct simulations and present a comparative analysis in graphical form with classical and integer derivatives. Results also demonstrate the impact of different parameters used in a model that is designed on the system, they provide more understanding and a better approach for real-life problems. Our results demonstrate the significant effects of toxic and fire activities produced by humans on forest ecosystems. More accurate management techniques are made possible by the modified ABC operator’s effectiveness in capturing the long-term effects of these disturbances. The findings highlight how crucial it is to use fractional calculus in ecological modeling to comprehend and manage the intricacies of forest preservation in the face of human pressures. To ensure the sustainable management of forest resources in the face of escalating environmental difficulties, this research offers policymakers and environmental managers a fresh paradigm for creating more robust and adaptive conservation policies.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012280","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 new technique for handling non-probability samples based on model-assisted kernel weighting","authors":"Beatriz Cobo ,&nbsp;Jorge Luis Rueda-Sánchez ,&nbsp;Ramón Ferri-García ,&nbsp;María del Mar Rueda","doi":"10.1016/j.matcom.2024.08.009","DOIUrl":"10.1016/j.matcom.2024.08.009","url":null,"abstract":"<div><p>Surveys are going through massive changes, and the most important innovation is the use of non-probability samples. Non-probability samples are increasingly used for their low research costs and the speed of the attainment of results, but these surveys are expected to have strong selection bias caused by several mechanisms that can eventually lead to unreliable estimates of the population parameters of interest. Thus, the classical methods of statistical inference do not apply because the probabilities of inclusion in the sample for individual members of the population are not known. Therefore, in the last few decades, new possibilities of inference from non-probability sources have appeared.</p><p>Statistical theory offers different methods for addressing selection bias based on the availability of auxiliary information about other variables related to the main variable, which must have been measured in the non-probability sample. Two important approaches are inverse probability weighting and mass imputation. Other methods can be regarded as combinations of these two approaches.</p><p>This study proposes a new estimation technique for non-probability samples. We call this technique model-assisted kernel weighting, which is combined with some machine learning techniques. The proposed technique is evaluated in a simulation study using data from a population and drawing samples using designs with varying levels of complexity for, a study on the relative bias and mean squared error in this estimator under certain conditions. After analyzing the results, we see that the proposed estimator has the smallest value of both the relative bias and the mean squared error when considering different sample sizes, and in general, the kernel weighting methods reduced more bias compared to based on inverse weighting. We also studied the behavior of the estimators using different techniques such us generalized linear regression versus machine learning algorithms, but we have not been able to find a method that is the best in all cases. Finally, we study the influence of the density function used, triangular or standard normal functions, and conclude that they work similarly.</p><p>A case study involving a non-probability sample that took place during the COVID-19 lockdown was conducted to verify the real performance of the proposed methodology, obtain a better estimate, and control the value of the variance.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378475424003094/pdfft?md5=9a932b624680104d7b919b9b781b865a&pid=1-s2.0-S0378475424003094-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142006756","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}

{"title":"A piecewise extreme learning machine for interface problems","authors":"Yijie Liang,&nbsp;Qinghui Zhang,&nbsp;Shaojie Zeng","doi":"10.1016/j.matcom.2024.08.008","DOIUrl":"10.1016/j.matcom.2024.08.008","url":null,"abstract":"<div><p>Deep learning methods have been developed to solve interface problems, benefiting from meshless features and the ability to approximate complex interfaces. However, existing deep neural network (DNN) methods for usual partial differential equations encounter accuracy limitations where after reaching a certain error level, further increases in network width, depth, and iteration steps do not enhance accuracy. This limitation becomes more notable in interface problems where the solution and its gradients may exhibit significant jumps across the interface. To improve accuracy, we propose a piecewise extreme learning machine (PELM) for addressing interface problems. An ELM is a type of shallow neural network where weight/bias coefficients in activation functions are randomly sampled and then fixed instead of being updated during the training process. Considering the solution jumps across the interface, we use a PELM scheme — setting one ELM function for each side of the interface. The two ELM functions are coupled using the interface conditions. Our numerical experiments demonstrate that the proposed PELM for the interface problem significantly improves the accuracy compared to conventional DNN solvers. The advantage of new method is shown for addressing interface problems that feature complex interface curves.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012281","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 of the deep BSDE method for stochastic control problems formulated through the stochastic maximum principle","authors":"Zhipeng Huang ,&nbsp;Balint Negyesi ,&nbsp;Cornelis W. Oosterlee","doi":"10.1016/j.matcom.2024.08.002","DOIUrl":"10.1016/j.matcom.2024.08.002","url":null,"abstract":"<div><p>It is well-known that decision-making problems from stochastic control can be formulated by means of a forward–backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. (2022) proposed an efficient deep learning algorithm based on the stochastic maximum principle (SMP). In this paper, we provide a convergence result for this deep SMP-BSDE algorithm and compare its performance with other existing methods. In particular, by adopting a strategy as in Han and Long (2020), we derive <em>a-posteriori estimate</em>, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. We present numerical examples for high-dimensional stochastic control problems, both in the cases of drift- and diffusion control, which showcase superior performance compared to existing algorithms.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150804","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":"Balancing individual and collective strategies: A new approach in metaheuristic optimization","authors":"Erik Cuevas ,&nbsp;Mario Vásquez ,&nbsp;Karla Avila ,&nbsp;Alma Rodriguez ,&nbsp;Daniel Zaldivar","doi":"10.1016/j.matcom.2024.08.004","DOIUrl":"10.1016/j.matcom.2024.08.004","url":null,"abstract":"<div><p>Metaheuristic approaches commonly disregard the individual strategies of each agent within a population, focusing primarily on the collective best solution discovered so far. While this methodology can yield promising results, it also has several significant drawbacks, such as premature convergence. This study introduces a new metaheuristic approach that emphasizes the balance between individual and social learning in agents. In this approach, each agent employs two strategies: an individual search technique performed by the agent and a social or collective strategy involving the best-known solution. The search strategy is considered a learning problem, and agents must adjust the use of both individual and social strategies accordingly. The equilibrium of this adjustment is determined by a counter randomly set for each agent, which determines the frequency of use invested in each strategy. This mechanism promotes diverse search patterns and fosters a dynamic and adaptive process, potentially improving problem-solving efficiency in intricate spaces. The proposed method was assessed by comparing it with several well-established metaheuristic algorithms using 21 test functions. The results demonstrate that the new method surpasses popular metaheuristic algorithms by offering superior solutions and attaining quicker convergence.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142020666","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":"Weak convergence of the split-step backward Euler method for stochastic delay integro-differential equations","authors":"Yan Li,&nbsp;Qiuhong Xu,&nbsp;Wanrong Cao","doi":"10.1016/j.matcom.2024.08.005","DOIUrl":"10.1016/j.matcom.2024.08.005","url":null,"abstract":"<div><p>In this paper, our primary objective is to discuss the weak convergence of the split-step backward Euler (SSBE) method, renowned for its exceptional stability when used to solve a class of stochastic delay integro-differential equations (SDIDEs) characterized by global Lipschitz coefficients. Traditional weak convergence analysis techniques are not directly applicable to SDIDEs due to the absence of a Kolmogorov equation. To bridge this gap, we employ modified equations to establish an equivalence between the SSBE method used for solving the original SDIDEs and the Euler–Maruyama method applied to modified equations. By demonstrating first-order strong convergence between the solutions of SDIDEs and the modified equations, we establish the first-order weak convergence of the SSBE method for SDIDEs. Finally, we present numerical simulations to validate our theoretical findings.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141990843","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":"Non-fragile control of discrete-time conic-type nonlinear Markovian jump systems under deception attacks using event-triggered scheme and Its application","authors":"M. Mubeen Tajudeen ,&nbsp;M. Syed Ali ,&nbsp;Ganesh Kumar Thakur ,&nbsp;Bandana Priya ,&nbsp;R. Perumal","doi":"10.1016/j.matcom.2024.08.007","DOIUrl":"10.1016/j.matcom.2024.08.007","url":null,"abstract":"<div><p>The non-fragile control issue of discrete-time conic-type nonlinear Markov jump systems under deception attacks has been investigated using an event-triggered method. The nonlinear terms satisfy the conic-type nonlinear constraint condition that lies in a known hypersphere with an uncertain center is employed. The deception attack may obstruct normal communication in an effort to obtain confidential information. In addition, a non-fragile event-triggered controller is suggested to further conserve communication resources. As a stochastic process, a deception attack is manageable by the established controller. Also, by choosing an appropriate Lyapunov-Krasovskii functional, a set of necessary conditions is found in terms of linear matrix inequalities (LMIs) that guarantee mean square stability of the discrete-time conic-type nonlinear Markov jump system in the presence of deception attacks. Finally, the proposed non-fragile event-triggered control techniques is validated with a DC-DC motor application system and another numerical example.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985160","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 transport with Lévy noise fully discrete numerical approximation","authors":"Andreas Stein ,&nbsp;Andrea Barth","doi":"10.1016/j.matcom.2024.07.036","DOIUrl":"10.1016/j.matcom.2024.07.036","url":null,"abstract":"<div><p>Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical finance, porous media, and pollution models often exhibit noise of a different nature. To capture temporal discontinuities and accommodate heavy-tailed distributions, Hilbert space-valued Lévy processes or Lévy fields are employed as driving noise terms. The numerical discretization of such SPDEs presents several challenges. The low regularity of the solution in space and time leads to slow convergence rates and instability in space/time discretization schemes. Furthermore, the Lévy process can take values in an infinite-dimensional Hilbert space, necessitating projections onto finite-dimensional subspaces at each discrete time point. Additionally, unbiased sampling from the resulting Lévy field may not be feasible. In this study, we introduce a novel fully discrete approximation scheme that tackles these difficulties. Our main contribution is a discontinuous Galerkin scheme for spatial approximation, derived naturally from the weak formulation of the SPDE. We establish optimal convergence properties for this approach and combine it with a suitable time stepping scheme to prevent numerical oscillations. Furthermore, we approximate the driving noise process using truncated Karhunen-Loève expansions. This approximation yields a sum of scaled and uncorrelated one-dimensional Lévy processes, which can be simulated with controlled bias using Fourier inversion techniques.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040764","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}