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Energy-stability and convergence of exponential difference schemes for extended Fisher-Kolmogorov equations 扩展Fisher-Kolmogorov方程指数差分格式的能量稳定性和收敛性
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-15 Epub Date: 2026-03-03 DOI: 10.1016/j.camwa.2026.02.013
Haoyue Jiang , Hai-wei Sun , Yanbin Tang , Dan Zhao
{"title":"Energy-stability and convergence of exponential difference schemes for extended Fisher-Kolmogorov equations","authors":"Haoyue Jiang ,&nbsp;Hai-wei Sun ,&nbsp;Yanbin Tang ,&nbsp;Dan Zhao","doi":"10.1016/j.camwa.2026.02.013","DOIUrl":"10.1016/j.camwa.2026.02.013","url":null,"abstract":"<div><div>This paper focuses on constructing and analyzing energy-stable schemes for the extended Fisher-Kolmogorov equation. The high-order difference methods are applied for the spatial discretization. And the exponential time difference (ETD) methods with a stabilized technique are used for the temporal discretization. Energy-stability of the fully-discrete scheme is proved. And the optimal <em>L</em><sup>2</sup> convergence results are obtained with help of the bounded numerical solutions and some inverse inequalities. Finally, several numerical experiments are presented to illustrate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 60-75"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147360835","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
High-Order nyström/Convolution-Quadrature solution of time-Domain scattering from closed and open lipschitz boundaries with dirichlet and neumann boundary conditions 具有dirichlet和neumann边界条件的封闭和开放lipschitz边界的时域散射的高阶nyström/卷积正交解
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-15 Epub Date: 2026-03-03 DOI: 10.1016/j.camwa.2026.01.039
Erli Wind-Andersen, Peter G. Petropoulos, Catalin Turc
{"title":"High-Order nyström/Convolution-Quadrature solution of time-Domain scattering from closed and open lipschitz boundaries with dirichlet and neumann boundary conditions","authors":"Erli Wind-Andersen,&nbsp;Peter G. Petropoulos,&nbsp;Catalin Turc","doi":"10.1016/j.camwa.2026.01.039","DOIUrl":"10.1016/j.camwa.2026.01.039","url":null,"abstract":"<div><div>We investigate high-order Convolution Quadratures methods for the solution of the wave equation in the exterior of two dimensional and axi-symmetric three dimensional scatterers that rely on Nyström discretizations for the Boundary Integral Equation formulations of the ensemble of associated Laplace domain modified Helmholtz problems. Both Dirichlet and Neumann boundary conditions, imposed on open-arc/open surfaces as well as Lipschitz closed scatterers, are considered. Two classes of CQ discretizations are employed, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nyström discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. A variety of accuracy tests are presented that showcase the high-order in time convergence (up to and including fifth order) that the Nyström CQ discretizations are capable of delivering and we compare to numerical results in the literature pertaining to time-domain multiple scattering problems solved with other methods.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 1-24"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359877","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
Generalized weak Galerkin methods for H(div), H(curl), and H(div, curl)-elliptic problems H(div)， H（旋度）和H（div，旋度）-椭圆问题的广义弱Galerkin方法
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-15 Epub Date: 2026-03-04 DOI: 10.1016/j.camwa.2026.02.018
Raman Kumar , Gouranga Pradhan
{"title":"Generalized weak Galerkin methods for H(div), H(curl), and H(div, curl)-elliptic problems","authors":"Raman Kumar ,&nbsp;Gouranga Pradhan","doi":"10.1016/j.camwa.2026.02.018","DOIUrl":"10.1016/j.camwa.2026.02.018","url":null,"abstract":"<div><div>This work presents a unified framework for generalized weak Galerkin (gWG) methods applied to two- and three-dimensional elliptic problems in the function spaces <strong>H</strong>(div), <strong>H</strong>(curl), and <strong>H</strong>(div, curl). The proposed methodology introduces generalized discrete differential operators, including weakly defined curl and divergence operators, within the weak Galerkin framework. A key feature of this approach is its flexibility in allowing arbitrary combinations of piecewise polynomial approximations in the interior and on the boundaries of each local polytopal element. Optimal order error estimates in energy norms are established for the resulting gWG method. Furthermore, numerical experiments are conducted to validate the theoretical findings and illustrate the accuracy and efficiency of the proposed method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 76-88"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147359871","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 three-level CIP-VEM approach for the Oseen equation Oseen方程的三级CIP-VEM方法
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-15 Epub Date: 2026-03-05 DOI: 10.1016/j.camwa.2026.02.014
M. Trezzi
{"title":"A three-level CIP-VEM approach for the Oseen equation","authors":"M. Trezzi","doi":"10.1016/j.camwa.2026.02.014","DOIUrl":"10.1016/j.camwa.2026.02.014","url":null,"abstract":"<div><div>We study a virtual element method for the Oseen problem. In the advection-dominated case, the method is stabilized with a three level jump of the convective term. To analyze the method, we prove specific estimates for the virtual space of potentials. Finally, we prove stability of the proposed method in the advection-dominated limit and derive <em>h</em>-version error estimates for the velocity and the pressure.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"210 ","pages":"Pages 113-136"},"PeriodicalIF":2.5,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147360624","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
Residual-type a posteriori error estimates for the Darcy-Forchheimer problem Darcy-Forchheimer问题的残差型后验误差估计
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.camwa.2026.01.040
María González, Hiram Varela
{"title":"Residual-type a posteriori error estimates for the Darcy-Forchheimer problem","authors":"María González,&nbsp;Hiram Varela","doi":"10.1016/j.camwa.2026.01.040","DOIUrl":"10.1016/j.camwa.2026.01.040","url":null,"abstract":"<div><div>We consider a primal-mixed finite element method proposed for the Darcy-Forchheimer model in [1]. We derive a new a posteriori error estimate and prove its reliability. We also provide some numerical experiments that show its performance in practice.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 28-43"},"PeriodicalIF":2.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162098","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
Adaptive isogeometric analysis with truncated hierarchical B-splines for nonlinear option pricing problems 非线性期权定价问题的截断层次b样条自适应等几何分析
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-01 Epub Date: 2026-02-14 DOI: 10.1016/j.camwa.2026.02.005
Ruo-Xi Yu
{"title":"Adaptive isogeometric analysis with truncated hierarchical B-splines for nonlinear option pricing problems","authors":"Ruo-Xi Yu","doi":"10.1016/j.camwa.2026.02.005","DOIUrl":"10.1016/j.camwa.2026.02.005","url":null,"abstract":"<div><div>This work develops an adaptive isogeometric analysis (IGA) framework based on truncated hierarchical B-spline (THB-spline) for pricing nonlinear multi-asset European options. The framework effectively handles both Black-Scholes and Heston stochastic volatility models by employing Newton linearization method for the nonlinear PDEs and the Crank-Nicolson scheme for temporal discretization. The discrete governing equation is derived via the Galerkin weighted residual method. A least-squares technique is utilized to accurately enforce initial and boundary conditions, while a smoothing-based error estimator drives the adaptive process. The precision and computational efficiency of the proposed framework are validated through comprehensive numerical analysis, establishing it as a robust tool for pricing multi-asset options with nonlinear features.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 44-56"},"PeriodicalIF":2.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146193031","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 error estimate of the second-order Crank–Nicolson leap-frog scheme for the phase field crystal model 相场晶体模型二阶Crank-Nicolson跳蛙格式的稳定性和误差估计
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-01 Epub Date: 2026-02-12 DOI: 10.1016/j.camwa.2026.01.042
Xiaozhuang Ma, Lizhen Chen
{"title":"Stability and error estimate of the second-order Crank–Nicolson leap-frog scheme for the phase field crystal model","authors":"Xiaozhuang Ma,&nbsp;Lizhen Chen","doi":"10.1016/j.camwa.2026.01.042","DOIUrl":"10.1016/j.camwa.2026.01.042","url":null,"abstract":"<div><div>In this paper, we propose an efficient, fully discrete numerical scheme for the phase field crystal model, combining second-order accuracy in time with spectral accuracy in space. First, we employ a multi-step strategy for time discretization, obtaining a second-order semi-discrete Crank–Nicolson leap-frog scheme. We rigorously prove that this scheme satisfies total mass conservation, unconditional energy stability, and linear, unique solvability. A detailed error analysis confirms its second-order convergence in time. Next, we discretize the semi-discrete scheme in space using the Fourier pseudo-spectral method, ensuring that the fully discrete scheme retains mass conservation and energy dissipation. Convergence and error estimates are also rigorously derived. Numerical experiments demonstrate the scheme’s accuracy and efficiency, particularly in capturing effective energy decay during long-time coarsening dynamics.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 1-15"},"PeriodicalIF":2.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162101","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
Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods 非拟合网格的通量逼近及其在多尺度混合混合方法中的应用
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-05-01 Epub Date: 2026-02-13 DOI: 10.1016/j.camwa.2026.01.016
T. Chaumont-Frelet , D. Paredes , F. Valentin
{"title":"Flux approximation on unfitted meshes and application to multiscale hybrid-mixed methods","authors":"T. Chaumont-Frelet ,&nbsp;D. Paredes ,&nbsp;F. Valentin","doi":"10.1016/j.camwa.2026.01.016","DOIUrl":"10.1016/j.camwa.2026.01.016","url":null,"abstract":"<div><div>The flux variable determines the approximation quality of hybridization-based numerical methods. This work proves that approximating flux variables in discontinuous polynomial spaces from the <em>L</em><sup>2</sup> orthogonal projection is super-convergent on meshes that are not necessarily aligned with jumping coefficient interfaces. The results assume only the local regularity of exact solutions in physical partitions. Based on the proposed flux approximation, we demonstrate that the mixed hybrid multiscale (MHM) finite element method is superconvergent on unfitted meshes, supporting the numerics presented in MHM seminal works.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"209 ","pages":"Pages 16-27"},"PeriodicalIF":2.5,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146162102","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 time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition 具有Neumann边界条件的半线性伪抛物方程的时变逆源问题
IF 2.5 2区 数学
Computers & Mathematics with Applications Pub Date : 2026-04-15 Epub Date: 2026-02-07 DOI: 10.1016/j.camwa.2026.01.038
Karel Van Bockstal , Khonatbek Khompysh
{"title":"A time-dependent inverse source problem for a semilinear pseudo-parabolic equation with Neumann boundary condition","authors":"Karel Van Bockstal ,&nbsp;Khonatbek Khompysh","doi":"10.1016/j.camwa.2026.01.038","DOIUrl":"10.1016/j.camwa.2026.01.038","url":null,"abstract":"<div><div>In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is recovered from the integral measurement over the domain Ω. Based on Rothe’s method, the existence and uniqueness of a weak solution, under suitable assumptions on the data, is established. A numerical time-discrete scheme for the unique weak solution and the unknown source coefficient is designed, and the convergence of the approximations is proven. Numerical experiments are presented to support the theoretical results. Noisy data is handled through polynomial regularisation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 97-112"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134759","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
Variable step-size IMEX scheme for a partial differential equation with delays and mixed derivative from option pricing under hard-to-borrow model 难借模型下具有时滞和混合导数的期权定价偏微分方程的变步长IMEX格式
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.2026.02.003
Yong Chen
{"title":"Variable step-size IMEX scheme for a partial differential equation with delays and mixed derivative from option pricing under hard-to-borrow model","authors":"Yong Chen","doi":"10.1016/j.camwa.2026.02.003","DOIUrl":"10.1016/j.camwa.2026.02.003","url":null,"abstract":"<div><div>This paper is devoted to the variable step-size implicit-explicit (IMEX) difference scheme for a partial differential equation (PDE) in two space dimensions with spatial delay term and mixed derivative term, which arises from the option pricing problem under hard-to-borrow stock model. First, a mesh-dependent Taylor expansion on nonuniform grids is proposed to approximate the spatial delay term. Second, the variable step-size IMEX scheme is constructed on nonuniform grids for both time and space. The consistency errors of the studied scheme are evaluated. Then, the theoretical results including unconditional stability and second-order convergence rates are established rigorously. Finally, some numerical examples support the theoretical analysis and show the efficacy of the proposed scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"208 ","pages":"Pages 113-126"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146152823","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
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