Mathematics and Computers in Simulation最新文献

英文中文

On the stability preserving of L1 scheme to nonlinear time-fractional Schrödinger delay equations

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-13 DOI: 10.1016/j.matcom.2024.11.020

Zichen Yao, Zhanwen Yang, Lixin Cheng

In this paper, we investigate the stability preserving of L1 scheme to nonlinear time fractional Schrödinger delay equations. This kind of Schrödinger equation contains both nonlocal effect and time memory reaction term. We derive sufficient conditions to ensure the asymptotic stability of the analytical equations. After that, we approximate the equations via the Galerkin finite element method in space. We show that the semidiscrete numerical solutions can inherit the long time behavior of the solutions. After that, a fully discrete approximation of the equations is obtained by the L1 scheme and a linear interpolation procedure. We provide detailed estimations on the discrete operators that are obtained by the Z transform and its inverse. Together with a discrete fractional comparison principle, we prove that the L1 scheme preserves the stability of the underlying equations. The main results obtained in this work do not depend on spatial and temporal step sizes. A numerical example confirms the effectiveness of our derived method and validates the theoretical findings.

引用次数: 0

Adaptive multilayer extreme learning machines

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-10 DOI: 10.1016/j.matcom.2024.12.004

Christos K. Filelis-Papadopoulos , John P. Morrison , Philip O’Reilly

Extreme learning machines is a neural network type that has been utilized in tasks such as regression and classification, due to their efficient training process, which is based on pseudoinverse matrices and randomized weights, avoiding the computationally intensive backpropagation. In order to further improve their performance and reduce their complexity with respect to number of required hyperparameters, especially in the case of multiple layer architectures, a novel multilayer adaptive approach, based on residual networks, is proposed. This approach constructs the network iteratively with respect to error minimization and parsimony using a recursive pseudoinverse matrix framework. A new block approach, using mixed precision arithmetic and Graphics Processing Units (GPU) is proposed. The proposed technique is coupled with a new adaptive penalty criterion to ensure adequate numbers of neurons are included in each layer, while avoiding highly correlated basis. Adaptive regularization, along with scaling, is also incorporated to ensure Symmetric Positive Definiteness (SPD) of the Gram matrix. Several random number distributions for the proposed approach are examined and discussed. Handling of large datasets is discussed and a new batch variant is proposed. The proposed scheme is evaluated for regression and classification tasks in a multitude of datasets and is compared with other neural network architectures.

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引用次数: 0

H∞ state estimation for fuzzy affine systems with PDT switching-based DoS attacks

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-07 DOI: 10.1016/j.matcom.2024.11.021

Hao Shen , Zhen Mei , Lei Su , Jing Wang , Kaibo Shi

The

H_{\infty}

state estimation problem for discrete-time Takagi–Sugeno (T–S) fuzzy-affine systems with Denial-of-Service (DoS) attacks whose occurrence is described by persistent dwell-time (PDT) switched model is discussed in this work. It should be noticed that distributed DoS attacks are characterized through proper configuration and categorization of mode, where the PDT switching strategy and the algorithm generating PDT switching sequence are proposed to describe the new framework. Correspondingly, the investigated system is transformed into the constrained PDT-switched system. Then, based on a piecewise and mode-dependent Lyapunov function, some sufficient conditions for obtaining the desirable estimator are proposed via the employed linear matrix inequality method and S-procedure theory, which guarantee that the resulting error system is exponentially stable and meets a prescribed

H_{\infty}

performance level. Finally, the effectiveness of the proposed method is illustrated by two numerical examples.

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引用次数: 0

Linear stability on transpiration effect of self-similar boundary layer flow for non-Newtonian fluids over a moving wedge

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-07 DOI: 10.1016/j.matcom.2024.11.016

Ramesh B. Kudenatti , Bharathi M.C. , Noor-E-Misbah

The two-dimensional boundary layer flow of non-Newtonian fluid over a wedge is numerically studied, in which the wedge is considered to be permeable and moving opposite or in the direction of the mainstream. The non-Newtonian fluid model is described by the power law and Carreau fluid. The equations governing fluid flow are nonlinear partial differential equations, which are then converted into ordinary differential equations for each fluid upon imposing suitable similarity transformations and assuming both wedge and mainstream velocity are expected to obey the power of distance. The Chebyshev collocation and shooting methods are utilized for the solutions to the boundary layer problem. Numerical results have shown that for a certain range of parameters, the solutions are not unique and do not exist to the model, leading to double solutions that are seen to satisfy the boundary conditions. This prompts us to assess the stability of the solutions as to which of these is practically encountered. The linear stability analysis applied on these double solutions shows that the first solution is always stable and hence practically realizable. The various physical reasons behind these results are discussed in some detail.

{"title":"Linear stability on transpiration effect of self-similar boundary layer flow for non-Newtonian fluids over a moving wedge","authors":"Ramesh B. Kudenatti , Bharathi M.C. , Noor-E-Misbah","doi":"10.1016/j.matcom.2024.11.016","DOIUrl":"10.1016/j.matcom.2024.11.016","url":null,"abstract":"<div><div>The two-dimensional boundary layer flow of non-Newtonian fluid over a wedge is numerically studied, in which the wedge is considered to be permeable and moving opposite or in the direction of the mainstream. The non-Newtonian fluid model is described by the power law and Carreau fluid. The equations governing fluid flow are nonlinear partial differential equations, which are then converted into ordinary differential equations for each fluid upon imposing suitable similarity transformations and assuming both wedge and mainstream velocity are expected to obey the power of distance. The Chebyshev collocation and shooting methods are utilized for the solutions to the boundary layer problem. Numerical results have shown that for a certain range of parameters, the solutions are not unique and do not exist to the model, leading to double solutions that are seen to satisfy the boundary conditions. This prompts us to assess the stability of the solutions as to which of these is practically encountered. The linear stability analysis applied on these double solutions shows that the first solution is always stable and hence practically realizable. The various physical reasons behind these results are discussed in some detail.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"231 ","pages":"Pages 46-61"},"PeriodicalIF":4.4,"publicationDate":"2024-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133226","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

A study on fractional centered difference scheme for high-dimensional integral fractional Laplacian operator with {ω}-circulant preconditioner

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-07 DOI: 10.1016/j.matcom.2024.12.002

Lot-Kei Chou , Wei Qu , Yuan-Yuan Huang , Siu-Long Lei

Fundamental properties for the coefficients of a second-order finite difference approximation of the fractional Laplacian in

d \geq 2

dimensions are derived in this paper. The obtained decay rate of the coefficients implies that the coefficients (with no closed-form expression) can be approximated via

d

-dimensional inverse fast Fourier transform of size

K

per dimension with accuracy

O (K^{- d - α})

, where

α \in (0, 2)

is the order of the fractional Laplacian. For solving fractional partial differential equations on regular grids, the coefficient matrix is a

d

-level Toeplitz matrix that can be preconditioned by the

d

-level

{ω}

-circulant matrix. Here, a spectral analysis of the difference matrix is derived. The purpose of this work is also to justify some observations presented by Hao et al. (2021). Numerical experiments in two-dimension and three-dimension illustrate that

{ω}

-circulant preconditioner has better performance over T. Chan’s circulant preconditioner.

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引用次数: 0

Topological data analysis for resilience assessment of water distribution networks

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-06 DOI: 10.1016/j.matcom.2024.12.001

Laura Selicato , Alessandro Pagano , Flavia Esposito , Matteo Icardi

Water Distribution Networks (WDNs) are critical assets, that are required to provide safe drinking water under a wide range of operational and management conditions, including failures. Understanding the structural properties of a water distribution system in different disruptive event scenarios is a key aspect of improving the security, reliability, and efficiency of the WDNs. In particular, the identification of critical components whose failure can negatively influence network performances and system resilience has direct relevance for decision-makers involved in planning, management, and improvement activities. The study of WDNs, structured as mathematical objects, can be carried on with different mathematical approaches. Among the many methods and tools available, the use of topological indicators and, in particular, Topological Data Analysis (TDA) has emerged as a cutting-edge tool in this field. In this work, we propose persistent homology to derive a new metric for the resilience of water networks, which, together with the other metrics known in the literature, can provide a more complete description of the system.

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引用次数: 0

Transmission dynamics of dengue with asymptomatic infection and a case study in Bangladesh

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-06 DOI: 10.1016/j.matcom.2024.12.003

Huarong Ren , Rui Xu

Dengue is a serious global public health crisis. The majority of dengue infections are asymptomatic, which makes disease control difficult. In this paper, a host–vector model considering asymptomatic infection and extrinsic and intrinsic incubation periods is developed to simulate the transmission pattern of dengue. The basic reproduction number is calculated by using the renewal equation method. The global threshold dynamics is established by constructing suitable Lyapunov functionals and using LaSalle’s invariance principle. The model is validated by fitting it to 2023 dengue epidemic data in Bangladesh. The fitting results show that the basic reproduction number is 4.1621 in the absence of control measures, in which contributions of asymptomatic infection and symptomatic infection account for 65% and 35%, respectively. In addition, through sensitivity analysis and numerical simulations, the effects of control measures and asymptomatic infection on basic reproduction number and transmission dynamics of dengue are clarified. The results show that (1) when the infectivity of asymptomatic individuals is more than 0.6 times that of symptomatic individuals, it is necessary to take measures to control the transmission risk of asymptomatic individuals; (2) the mortality rate of mosquito is the most critical factor in controlling dengue; (3) the mosquito density threshold for preventing mass transmission of dengue is 0.5199.

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引用次数: 0

A stabilizer-free weak Galerkin finite element method for an optimal control problem of a time fractional diffusion equation

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-05 DOI: 10.1016/j.matcom.2024.11.019

Shuo Wang , Jie Ma , Ning Du

This paper proposes a fully discrete stabilizer-free weak Galerkin (SFWG) finite element approximation for an optimal control problem driven by a time fractional diffusion equation. We focus on the spatial discretization of the SFWG finite element approximation to establish a semi-discrete scheme, followed by the application of L1 discretization to the Caputo fractional derivative in time to derive a fully discrete scheme. We then prove a priori error estimate for the discrete schemes. To reduce the computational complexity, we incorporate the proper orthogonal decomposition (POD) technique on the state and adjoint state systems to obtain a fully discrete reduced-order stabilizer-free weak Galerkin (ROSFWG) finite element method. Finally, the validity of the theoretical analysis is confirmed through numerical experiments.

引用次数: 0

Multi-objective model for residential energy management in context of individual self-consumption

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-04 DOI: 10.1016/j.matcom.2024.11.017

Sérgio Ramos , Luís A.C. Roque , António Gomes , João Soares , José Calvo Rolle , Zita Vale

The European Union (EU) strongly urged its member states to take action to establish energy communities. Domestic consumers now have the opportunity to organize themselves to play an active and decisive role in the electricity supply chain and make a solid contribution to an ecological footprint. This work proposes residential energy management, considering renewable resources production (photovoltaic panels) and energy storage systems for individual self-consumption approach and boosting future participation in energy community interactions. A multi-objective optimization model using Biased Random Key Genetic Algorithm (BRKGA) was adapted and implemented to minimize electricity consumption costs and maximize self-consumption usage. An energy storage system with 10 kW was considered to optimize electricity management. Two scenarios were proposed, one considering a residential prosumer with a photovoltaic (PV) power installed value of 3.56kWp and the other with 4.20kWp. The results showed a reduction in electricity consumption between 7 % and 8 % and an increase in self-consumption supported by a battery energy storage system of nearly 50 %. Data from an actual system were used to obtain realistic scenarios.

{"title":"Multi-objective model for residential energy management in context of individual self-consumption","authors":"Sérgio Ramos , Luís A.C. Roque , António Gomes , João Soares , José Calvo Rolle , Zita Vale","doi":"10.1016/j.matcom.2024.11.017","DOIUrl":"10.1016/j.matcom.2024.11.017","url":null,"abstract":"<div><div>The European Union (EU) strongly urged its member states to take action to establish energy communities. Domestic consumers now have the opportunity to organize themselves to play an active and decisive role in the electricity supply chain and make a solid contribution to an ecological footprint. This work proposes residential energy management, considering renewable resources production (photovoltaic panels) and energy storage systems for individual self-consumption approach and boosting future participation in energy community interactions. A multi-objective optimization model using Biased Random Key Genetic Algorithm (BRKGA) was adapted and implemented to minimize electricity consumption costs and maximize self-consumption usage. An energy storage system with 10 kW was considered to optimize electricity management. Two scenarios were proposed, one considering a residential prosumer with a photovoltaic (PV) power installed value of 3.56kWp and the other with 4.20kWp. The results showed a reduction in electricity consumption between 7 % and 8 % and an increase in self-consumption supported by a battery energy storage system of nearly 50 %. Data from an actual system were used to obtain realistic scenarios.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"231 ","pages":"Pages 120-127"},"PeriodicalIF":4.4,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133383","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

Observer-based self-triggered adaptive decentralized control for uncertain interconnected nonlinear systems

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2024-12-04 DOI: 10.1016/j.matcom.2024.11.018

Yaxin An, Yongchao Liu

In this paper, an observer-based self-triggered adaptive decentralized control method is presented for uncertain interconnected nonlinear systems (UINS) with unmeasured states. First, an adaptive state observer is constructed to estimate unmeasured system states. Then, the observer-based self-triggered controller is developed by applying the famous backstepping technique, in which the controller signal is updated based on the well-designed self-triggered protocol. Moreover, parameter adaptive laws are designed to address unknown parameters of UINS. Lyapunov theory is employed to prove that all signals of the UINS are semi-globally uniformly ultimately bounded (SGUUB) and the Zeno behavior will not appear. Simulation results manifest the efficacy of the derived self-triggered control solution.

引用次数: 0

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