Computers & Mathematics with Applications最新文献

{"title":"Conformal mapping based Physics-informed neural networks for designing neutral inclusions","authors":"Daehee Cho ,&nbsp;Hyeonmin Yun ,&nbsp;Jae Yong Lee ,&nbsp;Mikyoung Lim","doi":"10.1016/j.camwa.2026.01.026","DOIUrl":"10.1016/j.camwa.2026.01.026","url":null,"abstract":"<div><div>We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 347-362"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110517","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":"Peristaltic transport of non-Newtonian hybrid nanofluid flow through an inclined porous tube under a magnetic field and thermal radiation in a fuzzy environment","authors":"Bivas Bhaumik ,&nbsp;Soumini Dolui ,&nbsp;Mrutyunjaya Sahoo ,&nbsp;Snehashish Chakraverty ,&nbsp;Soumen De","doi":"10.1016/j.camwa.2026.01.020","DOIUrl":"10.1016/j.camwa.2026.01.020","url":null,"abstract":"<div><div>In advanced studies of bionanoscience, magnetic nanomaterials serve as therapeutic transporters for treating vascular disorders, such as carotid and peripheral artery diseases, along with other biomedical applications. This study explores the theoretical behavior of hybrid nanoparticles (Cu-Fe₂O₃) in two-dimensional peristaltic blood flow through an inclined, catheterized artery, accounting for outer wall slip in an uncertain environment. The non-Newtonian Jeffrey nanofluid model is employed, incorporating nonlinear thermal radiation and an externally induced magnetic field to capture novel aspects of nanofluid behavior. However, uncertainty in velocity and temperature patterns may arise due to variations in nanoparticle volume fraction, which cannot be ignored. To address this, these distributions are analyzed within a fuzzy framework, treating them as triangular fuzzy numbers (TFNs). Within this framework, the dimensionless nonlinear flow equations are converted into fuzzy differential equations by introducing symmetrical TFNs, where the nanoparticle volume fractions serve as fuzzy parameters. The Homotopy Perturbation Method (HPM) is then applied to derive fuzzy semi analytical solutions for temperature and velocity profiles using a double parametric approach for fuzzy numbers. Additionally, a comprehensive graphical analysis is presented, incorporating triangular fuzzy representations in both two-dimensional (2D) and three-dimensional (3D) frameworks for the fuzzy solutions of temperature and velocity profiles. The obtained fuzzy solutions are validated by comparing a special case of the present solution with existing precise solutions. An in-depth analysis of key flow characteristics such as wall shear stress, the Nusselt number, and the skin friction coefficient is conducted for the special case under various emerging parameters. It is observed that as the Darcy parameter increases, both the upper and lower bounds of fuzzy velocity improve. Meanwhile, an increase in the thermal radiation parameter leads to a significant drop in the fuzzy temperature profile due to enhanced heat dissipation through radiation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 280-300"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014493","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":"Modified quadrature method for solving three-dimensional axisymmetric boundary integral equations based on two extrapolations","authors":"Hu Li ,&nbsp;Jin Huang ,&nbsp;Yanying Ma","doi":"10.1016/j.camwa.2025.12.028","DOIUrl":"10.1016/j.camwa.2025.12.028","url":null,"abstract":"<div><div>This paper study the numerical solutions for three-dimensional axisymmetric boundary integral equations. First, a quadrature method achieving <em>O</em>(<em>h</em>³) accuracy with low computational complexity is developed. Convergence is proven using the compact operator theory. An error analysis yields a single-parameter asymptotic expansion with odd powers, enabling the creation of extrapolation algorithms to enhance accuracy. After one extrapolation, accuracy improves to <em>O</em>(<em>h</em>⁵), and further improvements are possible with using extrapolation again. Three numerical examples illustrate the algorithm’s efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 16-28"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886222","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":"Two unconditionally energy stable schemes for the Cahn-Hilliard equation","authors":"Jie Zhou ,&nbsp;Xuelian Jiang ,&nbsp;Ying Liu","doi":"10.1016/j.camwa.2025.12.010","DOIUrl":"10.1016/j.camwa.2025.12.010","url":null,"abstract":"<div><div>In this paper, we propose two fully discrete convex splitting schemes to solve the Cahn-Hilliard equation based on the mixed finite element method. For these two numerical schemes, the first-order backward Euler method and the second-order backward differentiation formula (BDF2) are used for temporal discretization, and the nonlinear term is treated by the convex splitting method. In order to ensure unconditional energy stability, the second-order time scheme requires the addition of a stability term <span><math><mrow><mo>−</mo><mi>β</mi><mi>τ</mi><mstyle><mi>Δ</mi></mstyle><mo>(</mo><msubsup><mi>φ</mi><mi>h</mi><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msubsup><mo>−</mo><msubsup><mi>φ</mi><mi>h</mi><mi>m</mi></msubsup><mo>)</mo></mrow></math></span>, where <em>β</em> ≥ 0 is a stable parameter. We strictly prove that both numerical schemes have unconditional energy stability. In particular, the second-order time scheme can be guaranteed to be unconditionally energy stable for <span><math><mrow><mi>β</mi><mo>≥</mo><mfrac><mn>1</mn><mn>16</mn></mfrac></mrow></math></span>. Additionally, we conduct rigorous error analysis on these two numerical schemes and obtain optimal error estimates in <em>H</em>₁ norm. Lastly, we verify the effectiveness of both numerical schemes and confirm the correctness of the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 29-57"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902644","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":"First- and second-order accurate, unconditionally energy gradient stable, uniquely solvable, and mass-preserving linear numerical schemes for Cahn–Hilliard equation with source term","authors":"Gyeonggyu Lee ,&nbsp;Seunggyu Lee","doi":"10.1016/j.camwa.2025.12.018","DOIUrl":"10.1016/j.camwa.2025.12.018","url":null,"abstract":"<div><div>The Cahn–Hilliard equation describes the phase separation phenomena at the microscale, such as those observed for diblock copolymers. However, its standard form is limited to capturing diverse real-world behaviors. To address this issue, we propose a structure-preserving Cahn–Hilliard equation with a generalized source term. Based on the total energy of the suggested total energy functional, the schemes were constructed using a linearly stabilized splitting method and a fast Fourier transform. A second-order extension was achieved using the implicit-explicit Runge–Kutta method. We prove the unique solvability, mass conservation, and energy gradient stability of both first- and second-order schemes. Temporal accuracy was validated through convergence tests. Numerical experiments further illustrate the phase behaviors under varying source term orders.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 1-15"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886221","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":"Mixed finite element method for a system of hemivariational inequalities of Navier-Stokes equations coupled with the heat equation","authors":"Hailing Xuan ,&nbsp;Wensi Wang ,&nbsp;Xiaoliang Cheng","doi":"10.1016/j.camwa.2026.01.013","DOIUrl":"10.1016/j.camwa.2026.01.013","url":null,"abstract":"<div><div>This paper explores a mixed finite element method for a system of hemivariational inequalities arising from the stationary Navier-Stokes equations coupled with the heat equation. The hemivariational inequalities system models the motion of a viscous incompressible fluid with thermal effects, where both the boundary conditions for the velocity and temperature fields involve the generalized Clarke gradient. We discuss the equivalence between different variational formulations and establish an existence theorem based on an alternative iterative approach and some results on hemivariational inequalities. The Navier-Stokes hemivariational inequalities system is solved using the mixed finite element method, and corresponding error estimates are derived. Numerical outcomes are presented based on the Uzawa method, which illustrates the optimal convergence rate as indicated by the error analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 212-227"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146000862","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":"An optimal ADMM for the contact problem between membranes","authors":"Shougui Zhang,&nbsp;Cairong Li,&nbsp;Yulu Duan","doi":"10.1016/j.camwa.2026.01.034","DOIUrl":"10.1016/j.camwa.2026.01.034","url":null,"abstract":"<div><div>An alternating direction method of multiplier (ADMM) based on an optimal choice of parameter is proposed for the contact problem between membranes. We use the finite-difference approximation for the problem and deduce a linear complementarity problem (LCP). Then the ADMM is employed to solve an equivalent saddle-point problem. We propose a optimal selection for the parameter, by a simple eigenvalue problem. Finally, experimental results demonstrate the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 334-346"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095741","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 family of upwind high-order finite volume methods for convection-diffusion problems on rectangular meshes","authors":"Renhui Teng ,&nbsp;Yonghai Li ,&nbsp;Hongtao Yang ,&nbsp;Qin Zhou ,&nbsp;Xia Cui","doi":"10.1016/j.camwa.2025.12.023","DOIUrl":"10.1016/j.camwa.2025.12.023","url":null,"abstract":"<div><div>We construct and analyze a family of upwind high-order finite volume schemes for convection-diffusion problems on rectangular meshes. The novelty is that for the upwind discretization of the convection term, we replace the trial function restricted to the dual boundary closest to the upstream element with the extension of the trial function from the upstream element. We prove coercivity and provide optimal error estimates in the <em>H</em>¹ and <em>L</em>² norms. The schemes achieve optimal convergence rates of order <em>k</em> in the <em>H</em>¹ norm and <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> in the <em>L</em>² norm, whether in diffusion-dominated or convection-dominated regimes. Numerical experiments confirm the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 80-96"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940428","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":"On the numerical solution of high-dimensional PDEs arising in multi-asset options via a kernel-type solver","authors":"Yanlai Song","doi":"10.1016/j.camwa.2025.12.027","DOIUrl":"10.1016/j.camwa.2025.12.027","url":null,"abstract":"<div><div>In this study, we present a numerical framework founded on a specialized version of radial basis function-produced finite difference solvers, designed for application in both interpolation tasks and the computational solution of higher-dimensional PDEs arising in multi-asset options. The distinguishing feature of the proposed method lies in its utilization of integrated forms of a special power of the multiquadric kernel to construct novel derivative weights, thereby enhancing solution accuracy and robustness. The derivative approximations are obtained through the derivation of analytical expressions, which are then evaluated on stencils comprising both uniformly spaced and non-uniformly distributed nodes. These formulations are constructed to offer greater flexibility in handling a wide spectrum of discretization patterns. Numerical results are provided to support the theoretical discussions.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 97-112"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940410","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 FE-MIFVE method for three-dimensional (3D) elliptic interface problems","authors":"Quanxiang Wang ,&nbsp;Jianqiang Xie ,&nbsp;Yu Zheng ,&nbsp;Liqun Wang","doi":"10.1016/j.camwa.2026.01.003","DOIUrl":"10.1016/j.camwa.2026.01.003","url":null,"abstract":"<div><div>In this paper, we propose a FE-MIFVE method for the solution of the three-dimensional elliptic interface problems on structured grids. The method uses the standard finite element discretization on regular elements, and uses the modified immersed finite volume element discretization on interface elements. By designing a suitable function which has the same jumps as the solution, we turn the original elliptic interface problem with nonhomogeneous jump conditions to be an elliptic interface problem with homogeneous jump conditions. Numerical experiments for various problems show the new proposed FE-MIFVE method can serve as an efficient field solver in a simulation on structured grids, such as predicting the electrostatics of solvated biomolecules.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"206 ","pages":"Pages 176-191"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957177","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}