Computers & Mathematics with Applications最新文献_第2页

An efficient high-order weak Galerkin finite element approach for Sobolev equation with variable matrix coefficients 变矩阵系数Sobolev方程的高效高阶弱Galerkin有限元法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-15 DOI: 10.1016/j.camwa.2025.01.013

Eric Ngondiep

{"title":"An efficient high-order weak Galerkin finite element approach for Sobolev equation with variable matrix coefficients","authors":"Eric Ngondiep","doi":"10.1016/j.camwa.2025.01.013","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.013","url":null,"abstract":"This paper constructs a high-order weak Galerkin finite element method for solving a two-dimensional Sobolev equation with variable matrix coefficients subjects to initial and boundary conditions. The proposed approach approximates the exact solution in time using interpolation techniques whereas the space derivatives are approximated by weak forms through integration by parts. The new algorithm is unconditionally stable, temporal second order convergence and spatial accurate with convergence order <mml:math altimg=\"si1.svg\"><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>, in the <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>;</mml:mo><mml:mspace width=\"0.20em\"></mml:mspace><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>-norm, where <ce:italic>p</ce:italic> is a nonnegative integer and <ce:italic>h</ce:italic> represents the grid space. The developed computational scheme is faster and more efficient than a broad range of numerical methods deeply studied in the literature for solving Sobolev problems. Some numerical examples are carried out to confirm the theory and to investigate the performance and validity of the constructed high-order numerical scheme.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"11 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020194","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

Constructive error estimates for a full-discretized periodic solution of heat equation by spatial finite-element and time spectral method 热方程全离散周期解的空间有限元和时间谱构造误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-13 DOI: 10.1016/j.camwa.2025.01.008

Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao

引用次数: 0

An efficient discontinuous Galerkin method for the hydro-dynamically coupled phase-field vesicle membrane model 水动力耦合相场囊泡膜模型的高效不连续伽辽金方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-13 DOI: 10.1016/j.camwa.2025.01.002

Zhaohua Li, Guang-an Zou, Lina Ma, Xiaofeng Yang

{"title":"An efficient discontinuous Galerkin method for the hydro-dynamically coupled phase-field vesicle membrane model","authors":"Zhaohua Li, Guang-an Zou, Lina Ma, Xiaofeng Yang","doi":"10.1016/j.camwa.2025.01.002","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.002","url":null,"abstract":"This paper presents a linear, fully-decoupled discontinuous Galerkin (DG) method for the flow-coupled phase-field vesicle membrane model. The fully discrete scheme is implemented by combining several reliable numerical techniques. Firstly, we employ the DG method for spatial discretization, which does not require that the numerical solutions are continuous across different grid cells, enabling adaptive treatment of complex vesicle membrane shapes and fluid flows. Secondly, to cope with nonlinear and coupling terms, scalar auxiliary variables (SAV) and implicit-explicit approaches are used, which improve numerical stability and computational efficiency. Finally, for the momentum equation, the pressure-correction method is used to assure the decoupling of velocity and pressure. Through rigorous mathematical proofs, this paper demonstrates the unconditional energy stability of the proposed scheme and derives its optimal error estimation. Numerical examples also show the method's effectiveness in terms of precision, energy stability, and simulated vesicle deformation in thin channels. The results highlight the method's potential application in fluid-coupled phase-field vesicle membrane models, while also providing new methodologies and technological support for numerical simulation and computational research in related domains.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"7 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986210","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

Regularization and finite element error estimates for elliptic distributed optimal control problems with energy regularization and state or control constraints 具有能量正则化和状态或控制约束的椭圆分布最优控制问题的正则化和有限元误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-13 DOI: 10.1016/j.camwa.2024.12.021

Peter Gangl, Richard Löscher, Olaf Steinbach

{"title":"Regularization and finite element error estimates for elliptic distributed optimal control problems with energy regularization and state or control constraints","authors":"Peter Gangl, Richard Löscher, Olaf Steinbach","doi":"10.1016/j.camwa.2024.12.021","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.021","url":null,"abstract":"In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the regularization parameter and the finite element mesh size in order to ensure an optimal balance between the error and the cost, and, on the discrete level, an optimal order of convergence which only depends on the regularity of the given target, also including discontinuous target functions. While in most cases, state or control constraints are discussed for the more common <mml:math altimg=\"si1.svg\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> regularization, much less is known in the case of energy regularizations. But in this case, and for both control and state constraints, we can formulate first kind variational inequalities to determine the unknown state, from which we can compute the control in a post processing step. Related variational inequalities also appear in obstacle problems, and are well established both from a mathematical and a numerical analysis point of view. Numerical results confirm the applicability and accuracy of the proposed approach.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"93 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986212","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

Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems 空间分数反应扩散系统基于受限pad<s:1>近似的傅立叶谱方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-13 DOI: 10.1016/j.camwa.2024.12.025

M. Yousuf, M. Alshayqi, S.S. Alzahrani

{"title":"Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems","authors":"M. Yousuf, M. Alshayqi, S.S. Alzahrani","doi":"10.1016/j.camwa.2024.12.025","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.025","url":null,"abstract":"By utilizing the power of the Fourier spectral approach and the restricted Padé rational approximations, we have devised two third-order numerical methods to investigate the complex phenomena that arise in multi-dimensional space fractional reaction-diffusion models. The Fourier spectral approach yields a fully diagonal representation of the fractional Laplacian with the ability to extend the methods to multi-dimensional cases with the same computational complexity as one-dimensional and makes it possible to attain spectral convergence. Third-order single-pole restricted Padé approximations of the matrix exponential are utilized in developing the time stepping methods. We also use sophisticated mathematical techniques, namely, discrete sine and cosine transforms, to improve the computational efficiency of the methods. Algorithms are derived from these methods for straight-forward implementation in one- and multidimensional models, accommodating both homogeneous Dirichlet and homogeneous Neumann boundary conditions. The third-order accuracy of these methods is proved analytically and demonstrated numerically. Linear error analysis of these methods is presented, stability regions of both methods are computed, and their graphs are plotted. The computational efficiency, reliability, and effectiveness of the presented methods are demonstrated through numerical experiments. The convergence results are computed to support the theoretical findings.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986211","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

Analysis and numerical approximation of a mathematical model for Aedes aegypti populations 埃及伊蚊种群数学模型的分析与数值逼近

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-10 DOI: 10.1016/j.camwa.2025.01.003

Anderson L.A. de Araujo, Jose L. Boldrini, Bianca M.R. Calsavara, Maicon R. Correa

{"title":"Analysis and numerical approximation of a mathematical model for Aedes aegypti populations","authors":"Anderson L.A. de Araujo, Jose L. Boldrini, Bianca M.R. Calsavara, Maicon R. Correa","doi":"10.1016/j.camwa.2025.01.003","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.003","url":null,"abstract":"We consider the rigorous analysis and the numerical approximation of a mathematical model for geographical spreading of <ce:italic>Aedes aegypti</ce:italic>. The complete model is composed of a system of parabolic partial differential equations coupled with one ordinary differential equation and has control terms related to the effects of insecticide application and sterile male release. The existence and uniqueness of solutions for the model are proven, and an efficient numerical methodology for approximating the unique solution of the mathematical model is proposed. The proposed numerical approach is based on a time-splitting scheme combined with locally conservative finite element methods. This combination of a well-posed mathematical model with a robust and efficient numerical formulation provides a suitable tool for the simulation of different scenarios of the spreading of <ce:italic>Aedes aegypti</ce:italic>. Numerical experiments, including a convergence study and a series of simulations that illustrate how the numerical model can be used in the decision-making process of controlling <ce:italic>Aedes aegypti</ce:italic> populations through the release of sterile male mosquitoes, assessing the responses to different inputs such as the total of sterile males released, the period for the release and locations for the intervention.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"23 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986228","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

Physics-informed neural networks with adaptive loss weighting algorithm for solving partial differential equations 具有自适应损失加权算法的物理信息神经网络求解偏微分方程

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-10 DOI: 10.1016/j.camwa.2025.01.007

Bo Gao, Ruoxia Yao, Yan Li

{"title":"Physics-informed neural networks with adaptive loss weighting algorithm for solving partial differential equations","authors":"Bo Gao, Ruoxia Yao, Yan Li","doi":"10.1016/j.camwa.2025.01.007","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.007","url":null,"abstract":"In recent years, physics-informed neural networks (PINNs) have garnered widespread attentions for the ability of solving nonlinear partial differential equations (PDE) using neural networks. The paper regards PINNs as multitask learning and proposes an adaptive loss weighting algorithm in physics-informed neural networks (APINNs). APINNs could balance the magnitudes of different loss functions during the training process to ensure a balanced contribution of parameters with different magnitudes to loss functions, thereby training solutions that satisfy initial boundary conditions and physical equations. Based on the original PINNs and APINNs, we respectively simulated the solitary wave solution of the Benjamin-Ono equation, the breather wave solution of the Sine-Gordon equation and the breather wave solution of the Mukherjee-Kundu equation. In the experiment of solving the solitary wave solution of the Benjamin-Ono equation, the minimum predict error of PINNs is about 60%, while the minimum predict error of APINNs is about 1%. As for solving breather wave solution, for the Sine-Gordon equation the minimum predict error of PINNs is around 10%, while the minimum predict error of APINNs is around 2%; and for the Mukherjee-Kundu equation, the minimum predict error of PINNs is about 30%, while the minimum predict error of APINNs is about 10%. The experimental results show that compared with PINNs, the predict solutions trained by APINNs have smaller errors.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"26 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986213","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 Lagrange multiplier method for fluid-structure interaction: Well-posedness and domain decomposition 流固耦合的拉格朗日乘子法：适定性和区域分解

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-10 DOI: 10.1016/j.camwa.2024.12.020

Amy de Castro, Hyesuk Lee, Margaret M. Wiecek

引用次数: 0

New insights into disease dynamics and treatment interventions with PID controller-based therapeutic strategies for pancreatic cancer 基于PID控制器的胰腺癌治疗策略对疾病动力学和治疗干预的新见解

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-09 DOI: 10.1016/j.camwa.2025.01.006

David Amilo, Khadijeh Sadri, Muhammad Farman, Evren Hincal, Kottakkaran Sooppy Nisar

{"title":"New insights into disease dynamics and treatment interventions with PID controller-based therapeutic strategies for pancreatic cancer","authors":"David Amilo, Khadijeh Sadri, Muhammad Farman, Evren Hincal, Kottakkaran Sooppy Nisar","doi":"10.1016/j.camwa.2025.01.006","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.006","url":null,"abstract":"In this paper, we developed a mathematical model for pancreatic cancer progression using a system of nonlinear partial differential equations (PDEs) with time delays, capturing disease dynamics in the human body. The model represents six key cell populations involved in pancreatic cancer: cancer cells (<ce:italic>C</ce:italic>), pancreatic stellate cells (<ce:italic>P</ce:italic>), stromal cells (<ce:italic>S</ce:italic>), extracellular matrix-degrading enzymes (<ce:italic>E</ce:italic>), tumor-associated macrophages (<ce:italic>N</ce:italic>), and immunosuppressive cells (<ce:italic>I</ce:italic>). For biological feasibility, we established model existence and uniqueness via the method of continuity and Banach's contraction principle, with global stability verified through the Lyapunov method. Sensitivity analysis identified critical factors such as cancer cell division, stromal cell activation, and immune cell infiltration, as targets for effective treatment. Optimal control and PID strategies demonstrated potential in limiting cancer proliferation and reprogramming the tumor microenvironment, while simulations highlighted the need for timely and sustained interventions. The results emphasize the importance of early surgery and immunomodulation in maximizing treatment efficacy, offering new insights into personalized and adaptive approaches to improve patient outcomes in pancreatic cancer treatment.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"49 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986227","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

Analysis of difference schemes for the Fokker–Planck angular diffusion operator Fokker-Planck角扩散算子的差分格式分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-01-09 DOI: 10.1016/j.camwa.2025.01.005

Óscar López Pouso, Javier Segura

引用次数: 0