Computers & Mathematics with Applications最新文献_第3页

Fractional spatio-temporal modeling for enhanced MRI super-resolution from multi-frame data 基于多帧数据增强MRI超分辨率的分式时空建模

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-15 Epub Date: 2026-02-12 DOI: 10.1016/j.camwa.2026.01.037

Anouar Ben-Loghfyry , Abderrahim Charkaoui , Shengda Zeng

{"title":"Fractional spatio-temporal modeling for enhanced MRI super-resolution from multi-frame data","authors":"Anouar Ben-Loghfyry , Abderrahim Charkaoui , Shengda Zeng","doi":"10.1016/j.camwa.2026.01.037","DOIUrl":"10.1016/j.camwa.2026.01.037","url":null,"abstract":"<div><div>This work presents an innovative spatio-temporal parabolic framework based on fractional calculus, employing both Caputo and Riemann–Liouville derivatives. The primary objective is to enhance traditional super-resolution methods, with a specific focus on multi-frame image reconstruction. The proposed model incorporates a spatially regularized fractional tensor diffusion mechanism that modulates both the magnitude and orientation of diffusion locally across the image domain. Theoretical analysis begins by addressing the model’s well-posedness. Using the Faedo-Galerkin scheme, we first establish the uniqueness and existence of weak solution to an auxiliary problem involving a time-fractional Caputo derivative. Then, leveraging Schauder fixed point theorem, we show the existence of a unique weak solution for our full model. Numerical experiments illustrate the practical capabilities of the approach, showcasing the advantages of fractional order methods in the context of image denoising and super-resolution. Furthermore, tests on real video sequences confirm the model’s robustness and performance in blind reconstruction scenarios. Comparative evaluations with state-of-the-art techniques underline the efficiency of our fractional model in terms of visual quality and detail preservation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 147-185"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146160706","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 simple-to-implement nonlinear preconditioning of Newton’s method for solving the steady Navier-Stokes equations 求解稳定Navier-Stokes方程的牛顿方法的一个简单实现的非线性预处理

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-15 Epub Date: 2026-02-11 DOI: 10.1016/j.camwa.2026.01.041

Muhammad Mohebujjaman , Mengying Xiao , Cheng Zhang

引用次数: 0

Free vibration analysis of laminated cylindrical shells based on the Walsh series method 基于Walsh级数法的层合圆柱壳自由振动分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-09 DOI: 10.1016/j.camwa.2026.02.001

Heyan Xu, Haichao Li, Fuzhen Pang, Tianyi Hang, Chuanshuai Yi

引用次数: 0

A positive and asymptotic preserving scheme for the linear transport equation on 2D unstructured meshes 二维非结构网格上线性输运方程的正渐近保持格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-29 DOI: 10.1016/j.camwa.2026.01.023

Clément Lasuen

引用次数: 0

A corrected Alikhanov scheme for a subdiffusion equation 亚扩散方程的修正Alikhanov格式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.014

Chaobao Huang , Yujie Yu , Na An , Hu Chen

{"title":"A corrected Alikhanov scheme for a subdiffusion equation","authors":"Chaobao Huang , Yujie Yu , Na An , Hu Chen","doi":"10.1016/j.camwa.2026.01.014","DOIUrl":"10.1016/j.camwa.2026.01.014","url":null,"abstract":"<div><div>This paper considers the subdiffusion equation with a weakly singular solution. To achieve the optimal accuracy with a smaller grading parameter <em>r</em> than that of the standard Alikhanov scheme, it’s essential to correct the Alikhanov scheme and the approximation <span><math><mrow><msup><mi>v</mi><mrow><mi>n</mi><mo>−</mo><mi>θ</mi></mrow></msup><mo>≈</mo><mi>θ</mi><msup><mi>v</mi><mi>n</mi></msup><mo>+</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>θ</mi><mo>)</mo></mrow><msup><mi>v</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span> (0 < <em>θ</em> < 1) by investigating the corrected terms <span><math><mrow><msubsup><mi>β</mi><mrow><mi>n</mi></mrow><mi>σ</mi></msubsup><mrow><mo>(</mo><msup><mi>v</mi><mn>1</mn></msup><mo>−</mo><msup><mi>v</mi><mn>0</mn></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msubsup><mi>μ</mi><mi>n</mi><mi>σ</mi></msubsup><mrow><mo>(</mo><msup><mi>v</mi><mn>1</mn></msup><mo>−</mo><msup><mi>v</mi><mn>0</mn></msup><mo>)</mo></mrow></mrow></math></span>, respectively. After that, the truncation error of the corrected Alikhanov scheme and the corrected approximation of <span><math><msup><mi>v</mi><mrow><mi>n</mi><mo>−</mo><mi>θ</mi></mrow></msup></math></span> are given. By adopting the corrected Alikhanov scheme for the Caputo derivative and the corrected approximation for <span><math><msup><mi>v</mi><mrow><mi>n</mi><mo>−</mo><mi>θ</mi></mrow></msup></math></span>, we construct a fully discrete scheme for the subdiffusion equation, employing a standard finite element method in space. Furthermore, the stability analysis and the optimal convergent analysis for the proposed scheme are investigated. Finally, numerical experiments are conducted to verify the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 15-26"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996271","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

Impact of partial magnetic field on natural convection in nanofluid-filled inclined cavities 局部磁场对纳米流体填充倾斜腔内自然对流的影响

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-02 DOI: 10.1016/j.camwa.2026.01.025

F.S. Oğlakkaya , C. Bozkaya

{"title":"Impact of partial magnetic field on natural convection in nanofluid-filled inclined cavities","authors":"F.S. Oğlakkaya , C. Bozkaya","doi":"10.1016/j.camwa.2026.01.025","DOIUrl":"10.1016/j.camwa.2026.01.025","url":null,"abstract":"<div><div>This study examines unsteady thermal convection of an Al<sub>2</sub>O<sub>3</sub>-water nanofluid in a differentially heated, wavy-walled inclined enclosure under a partially applied magnetic field. Utilizing a two-level time integration scheme combined with the dual reciprocity boundary element method (DRBEM) in space, the research investigates the impact of key parameters, including a wide range of Rayleigh and Hartmann numbers, magnetic field width, cavity inclination angle, number of undulations of wavy walls, and nanofluid solid volume fraction, on the flow dynamics and heat transfer. DRBEM approach, which focuses only on the boundary discretization, enables efficient numerical analysis while reducing computational load. Results presented through streamlines, isotherms, and average Nusselt number, reveal that increasing Hartmann number suppresses the convective motion, leading to a reduction of average Nusselt number, while increasing the Rayleigh number or nanoparticle concentration intensifies the heat transfer rate in enclosures with both flat and wavy-walls. The highest thermal performance is obtained when the enclosure with flat walls is tilted by a right angle under the presence of partially applied magnetic field for various combinations of the governing parameters. This research provides a comprehensive understanding of how multi-physical parameters and a partially applied magnetic field influence thermal convection, particularly within complex geometries, thereby contributing to advancements in the design and analysis of thermal systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 184-203"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110516","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

Stability and convergence of high-order WENO-OS scheme for the Allen-Cahn equation Allen-Cahn方程高阶WENO-OS格式的稳定性和收敛性

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-01 DOI: 10.1016/j.camwa.2026.01.030

Chun-Hua Zhang , Long Kuang , Wen-Ping Yuan , Xiang Wang

引用次数: 0

A hybrid MR-WENO scheme with a simplified troubled-cell indicator for hyperbolic conservation laws 双曲型守恒律的带有简化故障单元指示器的MR-WENO混合方案

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-19 DOI: 10.1016/j.camwa.2026.01.017

Jinming Zhang , Zhanjing Tao , Jun Zhu , Jianxian Qiu

引用次数: 0

Mixed-primal and fully-mixed formulations for the convection-diffusion-reaction system based upon Brinkman–Forchheimer equations 基于Brinkman-Forchheimer方程的对流-扩散-反应系统的混合原始和完全混合公式

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-02-20 DOI: 10.1016/j.camwa.2026.02.009

Alonso J. Bustos , Sergio Caucao , Gabriel N. Gatica

{"title":"Mixed-primal and fully-mixed formulations for the convection-diffusion-reaction system based upon Brinkman–Forchheimer equations","authors":"Alonso J. Bustos , Sergio Caucao , Gabriel N. Gatica","doi":"10.1016/j.camwa.2026.02.009","DOIUrl":"10.1016/j.camwa.2026.02.009","url":null,"abstract":"<div><div>We introduce and analyze new mixed formulations, within Banach space-based frameworks, for numerically solving the model given by the coupling of the Brinkman–Forchheimer equations with a convection-diffusion-reaction phenomenon. Specifically, for the former, we consider a pseudostress-velocity mixed formulation, whereas for the latter we analyze both primal and mixed approaches. In particular, for the mixed one the convection-diffusion-reaction part is reformulated by introducing the diffusion vector as an additional unknown, thus leading to a fully-mixed formulation of the coupling. On the other hand, in the mixed-primal setting, the Dirichlet boundary condition for the concentration is enforced through a suitable Lagrange multiplier, whereas this requirement is avoided in the fully mixed approach. We establish the well-posedness of both formulations using a fixed-point strategy and prove the well-posedness of the uncoupled problems by relying on recently established solvability results for perturbed saddle-point problems in Banach spaces, together with the Banach–Nečas–Babuška theorem and the Babuška–Brezzi theory. Additionally, we provide a discrete analysis for both approaches under specific hypotheses on arbitrary finite element spaces. For instance, for each integer <em>k</em> ≥ 0, we consider tensor and vector Raviart–Thomas subspaces of order <em>k</em> for the pseudostress and the diffusion, respectively, along with piecewise polynomial subspaces of degree  ≤ <em>k</em> for the velocity and concentration. This choice yields stable Galerkin schemes for the fully-mixed approach, for which optimal theoretical convergence rates are achieved. Finally, we illustrate the theoretical results through several numerical examples, comparing both approaches and discussing the advantages of each.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 222-249"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777698","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

MS-PINN: A physics-informed neural network for multi-field coupled evolution modeling in metal solidification MS-PINN：用于金属凝固多场耦合演化建模的物理信息神经网络

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2026-04-01 Epub Date: 2026-01-20 DOI: 10.1016/j.camwa.2026.01.015

Chen Bai , Yunhu Zhang , Hongxing Zheng , Quan Qian

{"title":"MS-PINN: A physics-informed neural network for multi-field coupled evolution modeling in metal solidification","authors":"Chen Bai , Yunhu Zhang , Hongxing Zheng , Quan Qian","doi":"10.1016/j.camwa.2026.01.015","DOIUrl":"10.1016/j.camwa.2026.01.015","url":null,"abstract":"<div><div>Simulating the metal solidification process is crucial for improving product quality, optimizing manufacturing processes, and developing new materials. Traditional numerical methods like the Finite Element Method (FEM) and Physics-Informed Neural Networks (PINNs) face significant challenges when applied to metal solidification simulations due to inefficiencies and inaccuracies in dealing with multiphysics coupling, nonlinearity, and spatio-temporal complexity. Despite their potential, PINNs require further optimization to accurately capture complex physical phenomena in practical simulations. In this study, we propose a novel method based on PINNs, termed MS-PINN, which integrates Fourier Feature Embedding (FFE), Residual-based Adaptive Resampling (RAD), and Self-adaptive Loss Balanced methods (SAL) to significantly enhance simulation accuracy and efficiency. FFE improves the model’s ability to capture high-frequency features, RAD increases learning efficiency in high-gradient regions, and SAL dynamically adjusts loss function weights to optimize the training process. Experimental results show that MS-PINN outperforms traditional PINNs and other advanced approaches, achieving average error reductions of approximately 81.00% compared to Conv-LSTM, 77.11% compared to TCN, and 61.56% compared to PINN in reconstruction experiments. In predictive experiments, MS-PINN reduces errors by 53.23%, 68.81%, and 72.54% compared to PINN, TCN, and CONV-LSTM methods, respectively. Additionally, we developed a general PDE-solving software, NeuroPDE, based on this method. NeuroPDE has demonstrated success not only in the solidification process of Cu-1wt.%Ag alloy but also in solving Burgers, diffusion, and Navier-Stokes (NS) equations, including turbulent datasets characterized by high Reynolds numbers, and their inverse problems. This highlights NeuroPDE’s versatility and broad applicability in solving complex forward and inverse problems in fluid dynamics and other fields.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"207 ","pages":"Pages 60-78"},"PeriodicalIF":2.5,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996321","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