Applied Numerical Mathematics最新文献_第4页

A new error analysis of an explicit skeletal discontinuous Galerkin scheme for time-dependent Maxwell equations 时变Maxwell方程的显式骨架不连续Galerkin格式的新误差分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-04 DOI: 10.1016/j.apnum.2025.05.011

Achyuta Ranjan Dutta Mohapatra, Bhupen Deka

{"title":"A new error analysis of an explicit skeletal discontinuous Galerkin scheme for time-dependent Maxwell equations","authors":"Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","doi":"10.1016/j.apnum.2025.05.011","DOIUrl":"10.1016/j.apnum.2025.05.011","url":null,"abstract":"<div><div>This article focuses on the convergence analysis of second-order time-dependent Maxwell equations in conducting and non-conducting media. Firstly, the spatial discretization is made using a skeletal discontinuous Galerkin method, and then some essential tools are established to deduce the stability and error estimates. Under suitable regularity assumptions on initial data, stability and optimal convergence of the error are proved for the semi-discrete problem in a discretely defined <span><math><mi>H</mi><mtext>(curl)</mtext></math></span>-norm. Next, temporal discretization is applied to the semi-discrete system by using the explicit Leap-frog schemes and optimal error bounds <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></math></span>, <span><math><mi>k</mi><mo>≥</mo><mn>1</mn></math></span> is the degree of polynomial approximation, are achieved in the discrete energy norm. Finally, computational experiments are performed to validate the theoretical conclusions. Error analysis of explicit fully discrete schemes in polygonal/polyhedral meshes for the second-order Maxwell equations in a conducting media is missing in the literature, and we intend to fill this gap in the current article.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 18-42"},"PeriodicalIF":2.2,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221744","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

Split-step θ-method for stochastic pantograph differential equations: Convergence and mean-square stability analysis 随机受电弓微分方程的裂步θ-法：收敛性和均方稳定性分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-02 DOI: 10.1016/j.apnum.2025.05.010

Fathalla A. Rihan, K. Udhayakumar

引用次数: 0

High-order numerical solution for solving multi-dimensional Schrödinger-Poisson equation 求解多维Schrödinger-Poisson方程的高阶数值解

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-27 DOI: 10.1016/j.apnum.2025.05.004

Maedeh Nemati, Mostafa Abbaszadeh, Mehdi Dehghan

{"title":"High-order numerical solution for solving multi-dimensional Schrödinger-Poisson equation","authors":"Maedeh Nemati, Mostafa Abbaszadeh, Mehdi Dehghan","doi":"10.1016/j.apnum.2025.05.004","DOIUrl":"10.1016/j.apnum.2025.05.004","url":null,"abstract":"<div><div>This paper explores the numerical solution of the Schrödinger-Poisson equation in one, two, and three dimensions, which has significant applications in quantum mechanics, cosmology, Bose-Einstein condensates, and nonlinear optics. To address the nonlinear aspects of the problem, we employ the split-step method, which decomposes the equation into linear and nonlinear components. The linear part is discretized using the compact finite difference (CFD) method, while the nonlinear component is solved exactly. For temporal discretization, we utilize the Crank-Nicolson method across all dimensions, achieving a second-order convergence rate of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>. Spatial discretization is carried out using a CFD scheme, ensuring a fourth-order convergence rate of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math></span>. In the case of two- and three-dimensional Schrödinger equations, the alternating direction implicit (ADI) method is applied. We establish that the proposed numerical schemes are convergent, unconditionally stable, and maintain the conservation of mass and energy at the discrete level. Numerical experiments in one, two, and three dimensions validate the effectiveness of our approach. Specifically, we compare the split-step CFD scheme with alternative methods, and for higher-dimensional cases, we evaluate the ADI-split-step CFD scheme against the standard split-step CFD method. The results demonstrate that the proposed methods significantly reduce computational time while maintaining accuracy.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 43-72"},"PeriodicalIF":2.2,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239999","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

An energy stable and well-balanced scheme for the Ripa system 里帕系统的能量稳定和平衡方案

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-23 DOI: 10.1016/j.apnum.2025.05.008

K.R. Arun , R. Ghorai

引用次数: 0

High-order and mass-conservative regularized implicit-explicit relaxation Runge-Kutta methods for the low regularity Schrödinger equations 低正则性Schrödinger方程的高阶和质量保守正则化隐显松弛龙格-库塔方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-22 DOI: 10.1016/j.apnum.2025.05.009

Jingye Yan , Hong Zhang , Yabing Wei , Xu Qian

引用次数: 0

Numerical analysis for an evolution equation with the p-biharmonic operator 具有p-双调和算子的演化方程的数值分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-22 DOI: 10.1016/j.apnum.2025.05.006

Rui M.P. Almeida , José C.M. Duque , Jorge Ferreira , Willian S. Panni

{"title":"Numerical analysis for an evolution equation with the p-biharmonic operator","authors":"Rui M.P. Almeida , José C.M. Duque , Jorge Ferreira , Willian S. Panni","doi":"10.1016/j.apnum.2025.05.006","DOIUrl":"10.1016/j.apnum.2025.05.006","url":null,"abstract":"<div><div>In this paper, we consider a parabolic equation with the <em>p</em>-biharmonic operator, where <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. By employing a suitable change of variable, we transform the fourth-order nonlinear parabolic problem into a system of two second-order differential equations. We investigate the properties of the discretized solution in spatial and temporal variables. Using the Brouwer fixed point theorem we prove the existence of the discretized solution. Through classical functional analysis techniques we demonstrate the uniqueness and a priori estimates of the discretized solution. We establish the order of convergence in space and time, we establish the relationship between the temporal variable and the spatial variable, ensuring the existence of the convergence order. Additionally, we highlight that the change in variable carried out is extremely advantageous, as it allows us to obtain the order of convergence for the solution and its higher order derivatives using only lower-degree polynomials. Finally, using the finite element method with Lagrange basis, we implement the computational codes in Matlab software, considering the one and two-dimensional cases. We present three examples to illustrate and validate the theory.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"216 ","pages":"Pages 164-186"},"PeriodicalIF":2.2,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134117","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

Sinc approximation method for solving system of singularly perturbed parabolic convection-diffusion equations 求解奇异摄动抛物型对流扩散方程组的Sinc逼近方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-21 DOI: 10.1016/j.apnum.2025.05.005

N. Barzehkar, A. Barati, R. Jalilian

引用次数: 0

A study of Cauchy problem of the Helmholtz equation based on a relaxation model: Regularization and analysis 基于松弛模型的亥姆霍兹方程柯西问题研究：正则化与分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-21 DOI: 10.1016/j.apnum.2025.05.007

Rongfang Gong , Xiaohui Liu , Catharine W.K. Lo , Gaocheng Yue

引用次数: 0

A second-order semi-implicit spectral deferred correction scheme for Cahn-Hilliard-Navier-Stokes equation Cahn-Hilliard-Navier-Stokes方程的二阶半隐式谱延迟校正格式

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-12 DOI: 10.1016/j.apnum.2025.05.003

Xin Liu , Dandan Xue , Shuaichao Pei , Hong Yang

引用次数: 0

On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems 求解对称特征值问题的贪婪随机坐标更新迭代方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-05-09 DOI: 10.1016/j.apnum.2025.04.010

Zhong-Zhi Bai

{"title":"On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems","authors":"Zhong-Zhi Bai","doi":"10.1016/j.apnum.2025.04.010","DOIUrl":"10.1016/j.apnum.2025.04.010","url":null,"abstract":"<div><div>In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"216 ","pages":"Pages 76-97"},"PeriodicalIF":2.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069908","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