Pub Date : 2025-11-07DOI: 10.1016/j.camwa.2025.10.024
JiangShan Tong, Zhong Chen, Wei Jiang
This article presents a novel meshless approach to solve a nonlinear fourth-order reaction-diffusion equation with the time-fractional derivative of Caputo-type on arbitrary bounded domains by constructing a set of novel basis using the Sinc function as a shape function with higher accuracy and stability. The key contributions and innovations of this study are summarized as follows. Firstly, the time non-smooth problem is addressed by discretizing time term and approximating the time-fractional derivative with the piecewise fractional linear interpolation. What's more, a novel approach has been developed for the superconvergence estimation of the two-dimensional Sinc function approximation. Subsequently, the time-iterative stability analysis of the semi-analytical solution is presented, and it is demonstrated that the solution is absolutely stable on arbitrary bounded domains. We then present a detailed analysis of both local and global error estimates and prove that the space-time convergence order is with M being the number of basis and q being the length of time step, that is, the spatial convergence order is superconvergent. At last, a series of numerical examples validates the effectiveness of the proposed meshless method, and the low CPU time demonstrates its high computational efficiency.
{"title":"Meshless approach for solving nonlinear time-fractional fourth-order reaction–diffusion equation with convergence order analysis and stability analysis","authors":"JiangShan Tong, Zhong Chen, Wei Jiang","doi":"10.1016/j.camwa.2025.10.024","DOIUrl":"10.1016/j.camwa.2025.10.024","url":null,"abstract":"<div><div>This article presents a novel meshless approach to solve a nonlinear fourth-order reaction-diffusion equation with the time-fractional derivative of Caputo-type on arbitrary bounded domains by constructing a set of novel basis using the Sinc function as a shape function with higher accuracy and stability. The key contributions and innovations of this study are summarized as follows. Firstly, the time non-smooth problem is addressed by discretizing time term and approximating the time-fractional derivative with the piecewise fractional linear interpolation. What's more, a novel approach has been developed for the superconvergence estimation of the two-dimensional Sinc function approximation. Subsequently, the time-iterative stability analysis of the semi-analytical solution is presented, and it is demonstrated that the solution is absolutely stable on arbitrary bounded domains. We then present a detailed analysis of both local and global error estimates and prove that the space-time convergence order is <span><math><mi>O</mi><mo>(</mo><mfrac><mrow><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn><mo>−</mo><mi>m</mi></mrow></msup></mrow><mrow><mi>q</mi></mrow></mfrac><mo>+</mo><mi>q</mi><mo>)</mo></math></span> with <em>M</em> being the number of basis and <em>q</em> being the length of time step, that is, the spatial convergence order is superconvergent. At last, a series of numerical examples validates the effectiveness of the proposed meshless method, and the low CPU time demonstrates its high computational efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"201 ","pages":"Pages 214-232"},"PeriodicalIF":2.5,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145461923","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}
In this study, we propose and examine a local discontinuous Galerkin finite element approach for solving the Kelvin-Voigt viscoelastic fluid flow equations, incorporating a forcing term within the space for . The method employs an upwind scheme to efficiently manage the nonlinear convective term. We establish new a priori bounds for the semidiscrete local discontinuous Galerkin approximations. Furthermore, we derive optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in -norm and the pressure approximation in -norm for . Assuming the smallness of the data, we also prove uniform error estimates in time. Additionally, we consider the first- and second-order backward difference schemes for full discretization and derive the corresponding fully discrete error estimates. Finally, numerical experiments are presented to support the theoretical findings.
{"title":"Local discontinuous Galerkin method for Kelvin-Voigt viscoelastic fluid flow model","authors":"Debendra Kumar Swain , Saumya Bajpai , Deepjyoti Goswami","doi":"10.1016/j.camwa.2025.10.025","DOIUrl":"10.1016/j.camwa.2025.10.025","url":null,"abstract":"<div><div>In this study, we propose and examine a local discontinuous Galerkin finite element approach for solving the Kelvin-Voigt viscoelastic fluid flow equations, incorporating a forcing term within the <span><math><msup><mrow><mtext>L</mtext></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> space for <span><math><mi>t</mi><mo>></mo><mn>0</mn></math></span>. The method employs an upwind scheme to efficiently manage the nonlinear convective term. We establish new <em>a priori</em> bounds for the semidiscrete local discontinuous Galerkin approximations. Furthermore, we derive optimal <em>a priori</em> error estimates for the semidiscrete discontinuous Galerkin velocity approximation in <span><math><msup><mrow><mtext>L</mtext></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and the pressure approximation in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm for <span><math><mi>t</mi><mo>></mo><mn>0</mn></math></span>. Assuming the smallness of the data, we also prove uniform error estimates in time. Additionally, we consider the first- and second-order backward difference schemes for full discretization and derive the corresponding fully discrete error estimates. Finally, numerical experiments are presented to support the theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 467-499"},"PeriodicalIF":2.5,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145434663","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}
Pub Date : 2025-11-03DOI: 10.1016/j.camwa.2025.10.026
Xiang Li , Du Zhou , Zihan Liu , Chao Xu , Likuan Chen , Bingliang Yan , Chuanjiang Shen , Zhixiong Wang , Henghu Yang , Yongzhi Zhao
Transient simulations offer the advantage of capturing time-dependent flow behavior, making them more suitable than steady simulations for modeling complex phenomena such as turbulence, vibration, cavitation, and noise. While traditional CFD methods are more suitable for handling steady simulations, they are less effective for transient simulations due to limited parallel processing capabilities, leading to high computational costs. As a result, the lattice Boltzmann method (LBM) is employed in this study, which is a more efficient approach for transient simulation owing to its efficient handling of complex geometries, programming simplicity, and strong parallel scalability. In order to enhance the stability of LBM in the numerical simulation of high Reynolds number flow fields, the multiple relaxation time (MRT) collision model and the Smagorinsky-Lilly large eddy simulation (LES) turbulence model are utilized. To address the high dissipation near the wall in the Lilly model, the van Driest damping function is incorporated, improving the accuracy of the LES model in boundary regions. Additionally, to minimize memory consumption and reduce computation time without sacrificing accuracy, wall functions and local grid refinement techniques are applied, reducing the overall number of computational grids required. An experimental platform was established to measure the flow characteristics of control valves, and the accuracy of the proposed method was validated by comparing the flow coefficient Cv at various valve openings. Finally, the effects of local grid refinement and wall functions on simulation accuracy were compared, demonstrating that these techniques significantly improve the precision of transient simulations.
{"title":"Transient numerical simulation of control valve flow characteristics using a wall function and local grid refinement in LES-LBM","authors":"Xiang Li , Du Zhou , Zihan Liu , Chao Xu , Likuan Chen , Bingliang Yan , Chuanjiang Shen , Zhixiong Wang , Henghu Yang , Yongzhi Zhao","doi":"10.1016/j.camwa.2025.10.026","DOIUrl":"10.1016/j.camwa.2025.10.026","url":null,"abstract":"<div><div>Transient simulations offer the advantage of capturing time-dependent flow behavior, making them more suitable than steady simulations for modeling complex phenomena such as turbulence, vibration, cavitation, and noise. While traditional CFD methods are more suitable for handling steady simulations, they are less effective for transient simulations due to limited parallel processing capabilities, leading to high computational costs. As a result, the lattice Boltzmann method (LBM) is employed in this study, which is a more efficient approach for transient simulation owing to its efficient handling of complex geometries, programming simplicity, and strong parallel scalability. In order to enhance the stability of LBM in the numerical simulation of high Reynolds number flow fields, the multiple relaxation time (MRT) collision model and the Smagorinsky-Lilly large eddy simulation (LES) turbulence model are utilized. To address the high dissipation near the wall in the Lilly model, the van Driest damping function is incorporated, improving the accuracy of the LES model in boundary regions. Additionally, to minimize memory consumption and reduce computation time without sacrificing accuracy, wall functions and local grid refinement techniques are applied, reducing the overall number of computational grids required. An experimental platform was established to measure the flow characteristics of control valves, and the accuracy of the proposed method was validated by comparing the flow coefficient <em>C<sub>v</sub></em> at various valve openings. Finally, the effects of local grid refinement and wall functions on simulation accuracy were compared, demonstrating that these techniques significantly improve the precision of transient simulations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"201 ","pages":"Pages 195-213"},"PeriodicalIF":2.5,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145434664","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}
Pub Date : 2025-10-30DOI: 10.1016/j.camwa.2025.10.019
Patrick Bammer, Lothar Banz, Andreas Schröder
In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linearly kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is conforming with respect to the displacement field and the plastic strain. Furthermore, the paper presents hp-finite element discretizations relying on a variational inequality as well as on a mixed variational formulation and discusses their equivalence by using biorthogonal basis functions. Numerical experiments demonstrate the applicability of the theoretical findings and underline the potential of h- and hp-adaptive finite element discretizations for problems of elastoplasticity.
{"title":"A posteriori error estimates for hp-FE discretizations in elastoplasticity","authors":"Patrick Bammer, Lothar Banz, Andreas Schröder","doi":"10.1016/j.camwa.2025.10.019","DOIUrl":"10.1016/j.camwa.2025.10.019","url":null,"abstract":"<div><div>In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linearly kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is conforming with respect to the displacement field and the plastic strain. Furthermore, the paper presents <em>hp</em>-finite element discretizations relying on a variational inequality as well as on a mixed variational formulation and discusses their equivalence by using biorthogonal basis functions. Numerical experiments demonstrate the applicability of the theoretical findings and underline the potential of <em>h</em>- and <em>hp</em>-adaptive finite element discretizations for problems of elastoplasticity.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 448-466"},"PeriodicalIF":2.5,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145404566","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}
Pub Date : 2025-10-30DOI: 10.1016/j.camwa.2025.10.017
Yuhao Zhang , Haifei Liu , Xiaoqiang Li , Yingjie Zhao , Jianxin Liu
This paper proposes the modified radial point interpolation method (M-RPIM) for solving the partial differential equations governing steady point current source fields. Unlike conventional RPIM, M-RPIM constructs support domains based on a cell, only one matrix inversion operation is needed when computing the shape functions in a integration cell, thereby improving computational efficiency. It determines the support domain by searching for neighboring cells layer by layer from the integration domain outward and controls the support domain range by adjusting the search depth. A systematic investigation of search depth effects on M-RPIM shape functions is conducted in this work. Numerical analysis demonstrates that the computational time of M-RPIM increases exponentially as the search depth increases, whereas the solution accuracy does not necessarily enhance. This work proves that M-RPIM with a search depth of 2 or 3 (employing approximately 15 support points) provides effective solutions for the partial differential equations governing steady point current source fields. When selecting a proper search depth, M-RPIM exhibits superior stability and accuracy compared to linear FEM, especially when dealing with complex geological models.
{"title":"Study on solving partial differential equations governing steady point current source field using M-RPIM","authors":"Yuhao Zhang , Haifei Liu , Xiaoqiang Li , Yingjie Zhao , Jianxin Liu","doi":"10.1016/j.camwa.2025.10.017","DOIUrl":"10.1016/j.camwa.2025.10.017","url":null,"abstract":"<div><div>This paper proposes the modified radial point interpolation method (M-RPIM) for solving the partial differential equations governing steady point current source fields. Unlike conventional RPIM, M-RPIM constructs support domains based on a cell, only one matrix inversion operation is needed when computing the shape functions in a integration cell, thereby improving computational efficiency. It determines the support domain by searching for neighboring cells layer by layer from the integration domain outward and controls the support domain range by adjusting the search depth. A systematic investigation of search depth effects on M-RPIM shape functions is conducted in this work. Numerical analysis demonstrates that the computational time of M-RPIM increases exponentially as the search depth increases, whereas the solution accuracy does not necessarily enhance. This work proves that M-RPIM with a search depth of 2 or 3 (employing approximately 15 support points) provides effective solutions for the partial differential equations governing steady point current source fields. When selecting a proper search depth, M-RPIM exhibits superior stability and accuracy compared to linear FEM, especially when dealing with complex geological models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 431-447"},"PeriodicalIF":2.5,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145404567","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}
Pub Date : 2025-10-28DOI: 10.1016/j.camwa.2025.10.013
Carlos Friedrich Loeffler , Jose Ronaldo Soares Ramos , Luciano de Oliveira Castro Lara , Thiago Galdino Balista , Julio Tomás Aquije Chacaltana
The Direct Interpolation Boundary Element Method (DIBEM) has proven to be a versatile, precise, and robust tool for transforming domain integrals into boundary integrals in the most diverse applications of the scalar field equation, such as the cases governed by the Equation of Stationary Poisson, Helmholtz, and Diffusion-Advection. DIBEM achieves this objective using radial basis functions to approximate the whole kernel of domain integrals composed of non-self-adjoint operators, frequently occurring in the mathematical modeling of complex problems. Using a simplified fundamental solution also allows for a more immediate and faster numerical solution without significantly losing precision in the results. In this work, DIBEM is used to solve transient heat transmission problems, which are governed by time-dependent partial differential equations and consist of one of the most important mathematical models for application in engineering, describing heat dissipation and absorption in equipment, machines, buildings, and metallurgical industrial processes, among others. Numerical tests evaluate the DIBEM model in two dimensions, in which different thermal loading variations over time, severe initial conditions, and accentuated variations in the diffusivity value are tested, aiming to assess the stability and consistency of the method.
{"title":"Solving transient heat conduction problems through the direct interpolation technique","authors":"Carlos Friedrich Loeffler , Jose Ronaldo Soares Ramos , Luciano de Oliveira Castro Lara , Thiago Galdino Balista , Julio Tomás Aquije Chacaltana","doi":"10.1016/j.camwa.2025.10.013","DOIUrl":"10.1016/j.camwa.2025.10.013","url":null,"abstract":"<div><div>The Direct Interpolation Boundary Element Method (DIBEM) has proven to be a versatile, precise, and robust tool for transforming domain integrals into boundary integrals in the most diverse applications of the scalar field equation, such as the cases governed by the Equation of Stationary Poisson, Helmholtz, and Diffusion-Advection. DIBEM achieves this objective using radial basis functions to approximate the whole kernel of domain integrals composed of non-self-adjoint operators, frequently occurring in the mathematical modeling of complex problems. Using a simplified fundamental solution also allows for a more immediate and faster numerical solution without significantly losing precision in the results. In this work, DIBEM is used to solve transient heat transmission problems, which are governed by time-dependent partial differential equations and consist of one of the most important mathematical models for application in engineering, describing heat dissipation and absorption in equipment, machines, buildings, and metallurgical industrial processes, among others. Numerical tests evaluate the DIBEM model in two dimensions, in which different thermal loading variations over time, severe initial conditions, and accentuated variations in the diffusivity value are tested, aiming to assess the stability and consistency of the method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 409-430"},"PeriodicalIF":2.5,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382501","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}
Pub Date : 2025-10-27DOI: 10.1016/j.camwa.2025.10.016
Xiangran Zheng , Qiang Wang , Wenxiang Sun , Yan Gu , Wenzhen Qu
This study presents a numerical framework with arbitrary-order accuracy for dynamic electroelastic analysis of two-dimensional (2D) and three-dimensional (3D) piezoelectric structures. The methodology achieves arbitrary-order convergence through a unified spatiotemporal coupling strategy. Temporal discretization is handled via the Krylov deferred correction (KDC) technique, which ensures asymptotically exact integration in time. For spatial approximation, the generalized finite difference method (GFDM) is employed, utilizing adaptive Taylor series expansions with matched orders to maintain consistency with temporal accuracy. An enhanced scheme is introduced for the enforcement of coupled electromechanical boundary conditions, improving numerical stability in cases where these conditions are not prescribed as explicit functions of time. To investigate the performance and reliability of the KDC-GFDM, four representative numerical examples are considered, covering both 2D and 3D cases with various geometric features and initial/boundary conditions. Numerically calculated results get systematically evaluated in comparison with available analytical solutions, when accessible, and with high-resolution reference solutions obtained from COMSOL Multiphysics.
{"title":"The general finite difference method with the Krylov deferred correction technique for dynamic 2D and 3D piezoelectric analysis","authors":"Xiangran Zheng , Qiang Wang , Wenxiang Sun , Yan Gu , Wenzhen Qu","doi":"10.1016/j.camwa.2025.10.016","DOIUrl":"10.1016/j.camwa.2025.10.016","url":null,"abstract":"<div><div>This study presents a numerical framework with arbitrary-order accuracy for dynamic electroelastic analysis of two-dimensional (2D) and three-dimensional (3D) piezoelectric structures. The methodology achieves arbitrary-order convergence through a unified spatiotemporal coupling strategy. Temporal discretization is handled via the Krylov deferred correction (KDC) technique, which ensures asymptotically exact integration in time. For spatial approximation, the generalized finite difference method (GFDM) is employed, utilizing adaptive Taylor series expansions with matched orders to maintain consistency with temporal accuracy. An enhanced scheme is introduced for the enforcement of coupled electromechanical boundary conditions, improving numerical stability in cases where these conditions are not prescribed as explicit functions of time. To investigate the performance and reliability of the KDC-GFDM, four representative numerical examples are considered, covering both 2D and 3D cases with various geometric features and initial/boundary conditions. Numerically calculated results get systematically evaluated in comparison with available analytical solutions, when accessible, and with high-resolution reference solutions obtained from COMSOL Multiphysics.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 382-408"},"PeriodicalIF":2.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382514","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}
Pub Date : 2025-10-27DOI: 10.1016/j.camwa.2025.10.018
Haoran Wang, Chuanjiang He
Low-light enhancement methods based on image Retinex yield enhanced images through the estimation of illumination and reflectance components. In image Retinex theory, since the reflectance component represents the reflectivity of objects' surface in the scene, it should be constrained between 0 and 1 to reflect its physical meaning. This constraint directly leads to an inequality constraint on the illumination component. Given the challenges of solving optimization problems with two inequality constraints, previous variational Retinex models initially treated these problems as unconstrained ones. To make up for the absence of constraints, hard projections are typically employed in the implementation algorithms. However, such a practice makes the models theoretically deviate from the physical essence of image Retinex and in practice may result in inaccurate estimates of two components, as shown in the analysis of this paper. For this problem, we propose a solution from the perspective of diffusion equations instead of the variational principle. Firstly, a general model for image Retinex is introduced in the framework of diffusion equations, where two inequality constraints are seamlessly incorporated into diffusion equations as source terms. To demonstrate the practicability of this general model, a Fractional-Integer order Diffusion system based on image Retinex (FIDR) is presented for low-light enhancement, which takes advantage of both integer-order diffusion preserving structure and fractional-order diffusion favoring texture. The FIDR is solved numerically by using an alternate iterative scheme based on explicit finite difference and 2D discrete Fourier transform. Subjective and objective evaluations on four low-light image datasets show that the FIDR model achieves higher performance in image decomposition and low-light enhancement, compared to several state-of-the-art methods.
{"title":"Fractional-integer order diffusion system based on image Retinex for low-light enhancement","authors":"Haoran Wang, Chuanjiang He","doi":"10.1016/j.camwa.2025.10.018","DOIUrl":"10.1016/j.camwa.2025.10.018","url":null,"abstract":"<div><div>Low-light enhancement methods based on image Retinex yield enhanced images through the estimation of illumination and reflectance components. In image Retinex theory, since the reflectance component represents the reflectivity of objects' surface in the scene, it should be constrained between 0 and 1 to reflect its physical meaning. This constraint directly leads to an inequality constraint on the illumination component. Given the challenges of solving optimization problems with two inequality constraints, previous variational Retinex models initially treated these problems as unconstrained ones. To make up for the absence of constraints, hard projections are typically employed in the implementation algorithms. However, such a practice makes the models theoretically deviate from the physical essence of image Retinex and in practice may result in inaccurate estimates of two components, as shown in the analysis of this paper. For this problem, we propose a solution from the perspective of diffusion equations instead of the variational principle. Firstly, a general model for image Retinex is introduced in the framework of diffusion equations, where two inequality constraints are seamlessly incorporated into diffusion equations as source terms. To demonstrate the practicability of this general model, a Fractional-Integer order Diffusion system based on image Retinex (FIDR) is presented for low-light enhancement, which takes advantage of both integer-order diffusion preserving structure and fractional-order diffusion favoring texture. The FIDR is solved numerically by using an alternate iterative scheme based on explicit finite difference and 2D discrete Fourier transform. Subjective and objective evaluations on four low-light image datasets show that the FIDR model achieves higher performance in image decomposition and low-light enhancement, compared to several state-of-the-art methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 364-381"},"PeriodicalIF":2.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382517","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}
Pub Date : 2025-10-27DOI: 10.1016/j.camwa.2025.10.023
Xiaofeng Wang , Weizhong Dai , Anjan Biswas
In this study, we have developed a conservative finite difference scheme that demonstrates fourth-order accuracy in space while preserving the discrete conservation of the invariant and energy for the Gardner equation with dual power-law nonlinearities in both 1D and 2D. Theoretical analyses and numerical results indicate that the proposed scheme achieves second-order accuracy in time and fourth-order accuracy in space. The solvability, stability and convergence of the difference scheme are rigorously analyzed using the discrete energy method. Additionally, experimental results are provided to illustrate the effectiveness of the proposed difference scheme in accurately capturing the dynamics of the Gardner equation in both 1D and 2D, as well as its reliability for long-term simulations.
{"title":"A conservative higher-order finite difference scheme for solving the Gardner equation with dual power-law nonlinearities in both 1D and 2D","authors":"Xiaofeng Wang , Weizhong Dai , Anjan Biswas","doi":"10.1016/j.camwa.2025.10.023","DOIUrl":"10.1016/j.camwa.2025.10.023","url":null,"abstract":"<div><div>In this study, we have developed a conservative finite difference scheme that demonstrates fourth-order accuracy in space while preserving the discrete conservation of the invariant <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and energy <span><math><msup><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for the Gardner equation with dual power-law nonlinearities in both 1D and 2D. Theoretical analyses and numerical results indicate that the proposed scheme achieves second-order accuracy in time and fourth-order accuracy in space. The solvability, stability and convergence of the difference scheme are rigorously analyzed using the discrete energy method. Additionally, experimental results are provided to illustrate the effectiveness of the proposed difference scheme in accurately capturing the dynamics of the Gardner equation in both 1D and 2D, as well as its reliability for long-term simulations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"201 ","pages":"Pages 171-194"},"PeriodicalIF":2.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382506","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}
Pub Date : 2025-10-27DOI: 10.1016/j.camwa.2025.10.021
Qian Yu , Musi Zeng , Chao Yang
We propose a second-order accurate scheme using the stabilized-energy quadratization approach based on the Crank-Nicolson method to solve the 2D material growth problem during the chemical vapor deposition process. We theoretically prove the local pseudo energy dissipation rate preserving property and the global pseudo energy dissipation property with the driven force under proper boundary conditions, which allows for a large time step to evolve. In the numerical experiments, we compare the proposed energy stable scheme with several popular numerical methods including two Euler schemes and a hybrid scheme to examine the performance in terms of stability, convergence and morphological evolution. The results show that the proposed scheme has an advantage in accuracy and stability. And the numerical simulations are consistent with the scanning electron microscopic images from lab experiments, which validates the proposed scheme in this work.
{"title":"A second-order accurate and energy-stable scheme for phase field simulations of chemical vapor deposition in 2D materials growth","authors":"Qian Yu , Musi Zeng , Chao Yang","doi":"10.1016/j.camwa.2025.10.021","DOIUrl":"10.1016/j.camwa.2025.10.021","url":null,"abstract":"<div><div>We propose a second-order accurate scheme using the stabilized-energy quadratization approach based on the Crank-Nicolson method to solve the 2D material growth problem during the chemical vapor deposition process. We theoretically prove the local pseudo energy dissipation rate preserving property and the global pseudo energy dissipation property with the driven force under proper boundary conditions, which allows for a large time step to evolve. In the numerical experiments, we compare the proposed energy stable scheme with several popular numerical methods including two Euler schemes and a hybrid scheme to examine the performance in terms of stability, convergence and morphological evolution. The results show that the proposed scheme has an advantage in accuracy and stability. And the numerical simulations are consistent with the scanning electron microscopic images from lab experiments, which validates the proposed scheme in this work.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 315-330"},"PeriodicalIF":2.5,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145382505","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}
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