Computers & Mathematics with Applications最新文献_第4页

A space-time discontinuous Petrov-Galerkin finite element formulation for a modified Schrödinger equation for laser pulse propagation in waveguides 激光脉冲在波导中传播的修正Schrödinger方程的时空不连续Petrov-Galerkin有限元公式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-18 DOI: 10.1016/j.camwa.2025.09.004

A. Chakraborty , J. Muñoz-Matute , L. Demkowicz , J. Grosek

引用次数: 0

Regular boundary element method for composite shear deformable plate and shell 复合剪切变形板壳的规则边界元法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-18 DOI: 10.1016/j.camwa.2025.09.016

W. Huang, X.B. Yan, J.X. Liao, L.K. Feng, P.H. Wen

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Source point selection in the MFS using orthogonal matching pursuit: Two-dimensional elastic wave scattering by a rectangular cavity 正交匹配追踪MFS中的源点选择：矩形腔体的二维弹性波散射

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-18 DOI: 10.1016/j.camwa.2025.09.003

Akira Furukawa

引用次数: 0

Convergence analysis of an energy-stable linearized virtual element method for the strongly damped Klein-Gordon equation 强阻尼Klein-Gordon方程能量稳定线性化虚元法的收敛性分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-18 DOI: 10.1016/j.camwa.2025.09.002

Zhixin Liu , Minghui Song , Yuhang Zhang

{"title":"Convergence analysis of an energy-stable linearized virtual element method for the strongly damped Klein-Gordon equation","authors":"Zhixin Liu , Minghui Song , Yuhang Zhang","doi":"10.1016/j.camwa.2025.09.002","DOIUrl":"10.1016/j.camwa.2025.09.002","url":null,"abstract":"<div><div>In this paper, we propose and analyze an efficient, linearized, fully discrete scheme for the nonlinear, strongly damped Klein-Gordon equation on polygonal meshes. The numerical scheme uses a conforming virtual element method for spatial discretization and a modified leapfrog (central finite difference) scheme for time discretization, with the nonlinear term <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi></math></span> is treated semi-implicitly. We first prove that the proposed scheme is energy dissipative in the sense of discrete energy, and then the stability of the numerical solution in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm is established using mathematical induction, which plays an important role in handling the nonlinear term. By applying the boundedness of the numerical solution and the Sobolev embedding inequality, we derive the optimal <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> error estimate of order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> without imposing any ratio restrictions between the time step <em>τ</em> and the mesh size <em>h</em>. Additionally, we remark that the leapfrog virtual element scheme can be applied to some more complex nonlinear damped wave equations. Finally, some numerical examples are provided to confirm the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 49-66"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093761","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 posteriori error estimate of the discontinuous Galerkin method with Lagrange multiplier for elliptic problems 椭圆型问题的带拉格朗日乘子的间断伽辽金方法的后验误差估计

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-17 DOI: 10.1016/j.camwa.2025.09.005

Mi-Young Kim

引用次数: 0

Stability and convergence analysis of mixed finite element approximations for a Biot-Brinkman model Biot-Brinkman模型混合有限元近似的稳定性和收敛性分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-17 DOI: 10.1016/j.camwa.2025.09.006

Wenlong He , Jiwei Zhang

引用次数: 0

A DOFs condensation based algorithm for solving saddle point systems in 2D contact computation 二维接触计算中基于自由度凝聚的鞍点方程组求解算法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-16 DOI: 10.1016/j.camwa.2025.08.032

Xiaoyu Duan , Zihan Wang , Hengbin An , Zeyao Mo

引用次数: 0

Physics-informed neural network for option pricing weather derivatives model 天气衍生品期权定价模型的物理信息神经网络

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-16 DOI: 10.1016/j.camwa.2025.09.001

Saurabh Bansal , Pradanya Boro , Srinivasan Natesan

{"title":"Physics-informed neural network for option pricing weather derivatives model","authors":"Saurabh Bansal , Pradanya Boro , Srinivasan Natesan","doi":"10.1016/j.camwa.2025.09.001","DOIUrl":"10.1016/j.camwa.2025.09.001","url":null,"abstract":"<div><div>Weather derivatives are financial tools that use a weather index as the underlying asset to provide protection against non-catastrophic weather events. In this article, we propose a physics-informed neural network (PINN) approach for pricing weather derivatives associated with two standard processes: the Ornstein-Uhlenbeck process and the Ornstein-Uhlenbeck process with jump-diffusions. PINNs are a scientific machine learning method specifically designed to address problems related to partial differential equations (PDEs).</div><div>To apply the PINN technique for jump-diffusion, we convert the partial integro-differential equation into a PDE using integral discretization. We randomly select training data points within the domain and utilize the transformed PDE along with the initial and boundary conditions to construct the loss function. For the neurons in the hidden layer, we employ the hyperbolic tangent function (tanh) as the activation function. The weights of the network connection are optimized using the L-BFGS algorithm.</div><div>We will conduct numerical experiments to evaluate the efficiency of the proposed technique. Additionally, we compare our method with conventional numerical approaches to show that our technique serves as an effective alternative to existing pricing methods for weather derivatives. Finally, we will examine a real-world case study where the model's parameters are determined using precipitation data.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 1-21"},"PeriodicalIF":2.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093766","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

Two-point stress approximation: A simple and robust finite volume method for linearized (poro-)elasticity and Stokes flow 两点应力近似：线性化（孔隙）弹性和斯托克斯流的一种简单而稳健的有限体积方法

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-12 DOI: 10.1016/j.camwa.2025.07.035

Jan Martin Nordbotten , Eirik Keilegavlen

引用次数: 0

Data-driven SFB solutions and parameters discovery for nonlinear Schrödinger equation via time domain decomposition physics-informed neural networks 基于时域分解物理信息的神经网络的非线性Schrödinger方程的数据驱动SFB解决方案和参数发现

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-12 DOI: 10.1016/j.camwa.2025.09.007

Jiaxin Chen , Biao Li , Manwai Yuen

{"title":"Data-driven SFB solutions and parameters discovery for nonlinear Schrödinger equation via time domain decomposition physics-informed neural networks","authors":"Jiaxin Chen , Biao Li , Manwai Yuen","doi":"10.1016/j.camwa.2025.09.007","DOIUrl":"10.1016/j.camwa.2025.09.007","url":null,"abstract":"<div><div>In this paper, we integrate domain decomposition techniques into the classical physics-informed neural networks (PINNs) by introducing interface training points, and propose a time domain decomposition PINNs (TDD-PINNs) framework. This model is applied to investigate the dynamic behaviour of solitons on finite background (SFB) solutions and parameter discovery in the nonlinear Schrödinger equation (NLSE). The TDD-PINNs is employed to study various SFB solutions, including the Akhmediev breather, Peregrine soliton, Kuznetsov-Ma soliton, as well as second- and third-order rogue waves. Experimental results demonstrate that, compared to classical PINNs, the proposed TDD-PINNs significantly reduce training time and improve prediction accuracy by one to two orders of magnitude. For inverse problems, the TDD-PINNs algorithm can accurately identify unknown parameters in the NLSE, both under noisy and noise-free conditions, addressing the complete failure of classical PINNs in parameter identification for NLSE and demonstrating strong robustness.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 45-63"},"PeriodicalIF":2.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050174","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