Applied Numerical Mathematics最新文献_第9页

Finite block method for nonlinear time-fractional partial integro-differential equations: Stability, convergence, and numerical analysis 非线性时间分数阶偏积分微分方程的有限块法：稳定性、收敛性和数值分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-03-20 DOI: 10.1016/j.apnum.2025.03.002

Amin Ghoreyshi , Mostafa Abbaszadeh , Mahmoud A. Zaky , Mehdi Dehghan

引用次数: 0

Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation 非局部Allen-Cahn方程的隐式积分因子法与pad<s:1>逼近策略

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-03-03 DOI: 10.1016/j.apnum.2025.02.019

Yuxin Zhang , Hengfei Ding

{"title":"Implicit integration factor method coupled with Padé approximation strategy for nonlocal Allen-Cahn equation","authors":"Yuxin Zhang , Hengfei Ding","doi":"10.1016/j.apnum.2025.02.019","DOIUrl":"10.1016/j.apnum.2025.02.019","url":null,"abstract":"<div><div>The space nonlocal Allen-Cahn equation is a famous example of fractional reaction-diffusion equations. It is also an extension of the classical Allen-Cahn equation, which is widely used in physics to describe the phenomenon of two-phase fluid flows. Due to the nonlocality of the nonlocal operator, numerical solutions to these equations face considerable challenges. It is worth noting that whether we use low-order or high-order numerical differential formulas to approximate the operator, the corresponding matrix is always dense, which implies that the storage space and computational cost required for the former and the latter are the same. However, the higher-order formula can significantly improve the accuracy of the numerical scheme. Therefore, the primary goal of this paper is to construct a high-order numerical formula that approximates the nonlocal operator. To reduce the time step limitation in existing numerical algorithms, we employed a technique combining the compact integration factor method with the Padé approximation strategy to discretize the time derivative. A novel high-order numerical scheme, which satisfies both the maximum principle and energy stability for the space nonlocal Allen-Cahn equation, is proposed. Furthermore, we provide a detailed error analysis of the differential scheme, which shows that its convergence order is <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></math></span>. Especially, it is worth mentioning that the fully implicit scheme with sixth-order accuracy in spatial has never been proven to maintain the maximum principle and energy stability before. Finally, some numerical experiments are carried out to demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 88-107"},"PeriodicalIF":2.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548519","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

Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping 具有非正变号核和非线性非局部阻尼的双曲型积分微分方程的数值逼近

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-26 DOI: 10.1016/j.apnum.2025.02.018

Wenlin Qiu , Xiangcheng Zheng , Kassem Mustapha

引用次数: 0

Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models Ripa模型平衡良好且保持正性的干湿锋重建方案

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.014

Xue Wang , Guoxian Chen

{"title":"Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models","authors":"Xue Wang , Guoxian Chen","doi":"10.1016/j.apnum.2025.02.014","DOIUrl":"10.1016/j.apnum.2025.02.014","url":null,"abstract":"<div><div>This paper explores the reconstruction of wet-dry fronts (WDF) for solving both one-dimensional (1D) and two-dimensional (2D) Ripa systems, with a particular emphasis on the influence of temperature. Our aim is to develop a well-balanced numerical scheme that not only preserves the steady state but also ensures the positivity of both water height and temperature. By employing conservative variables for reconstruction instead of equilibrium variables, we have achieved a significant doubling of the CFL number for fully flooded cells. We have refined the original 1D WDF reconstruction method and further enhanced the corresponding 2D scheme. The conservation principle and linearity observed in the wet region of partially flooded cells indicate a constant cell-wise velocity and temperature. Additionally, we introduce a novel draining time approach to adjust the numerical flux in an upwind manner, ensuring both stability and efficiency, even for partially flooded cells. Numerical examples are presented to demonstrate the well-balanced property, high-order accuracy, and positivity-preserving characteristics of our proposed method. These examples also showcase the method's ability to capture small perturbations in the lake-at-rest steady state, highlighting its potential for practical applications.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 38-60"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507961","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 tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems （p,q）-五对角线性系统的基于三对角化的任意步长约简方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.017

Yi-Fan Wang, Ji-Teng Jia, Xin Fan

引用次数: 0

Drug release from polymeric platforms for non smooth solutions 非光滑溶液的聚合物平台药物释放

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.016

J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi

{"title":"Drug release from polymeric platforms for non smooth solutions","authors":"J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi","doi":"10.1016/j.apnum.2025.02.016","DOIUrl":"10.1016/j.apnum.2025.02.016","url":null,"abstract":"<div><div>This paper aims to conclude a sequence of works focused in the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>- functions. In the present work, our aim is to establish second order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>- functions. Numerical experiments illustrating the obtained theoretical results are also included.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 12-37"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508679","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 novel projection-based method for monotone equations with Aitken Δ2 acceleration and its application to sparse signal restoration 一种新的具有Aitken Δ2加速度的单调方程投影方法及其在稀疏信号恢复中的应用

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.013

Ahmad Kamandi

引用次数: 0

Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations 抛物型方程弱Galerkin有限元变时步BDF2隐式格式的收敛性分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.015

Chenxing Li , Fuzheng Gao , Jintao Cui

引用次数: 0

A decoupled nonconforming finite element method for biharmonic equation in three dimensions 三维双调和方程的解耦非协调有限元法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.012

Xuewei Cui, Xuehai Huang

引用次数: 0

A mixed discontinuous Galerkin method for the Biot equations Biot方程的混合不连续Galerkin方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.011

Jing Wen

{"title":"A mixed discontinuous Galerkin method for the Biot equations","authors":"Jing Wen","doi":"10.1016/j.apnum.2025.02.011","DOIUrl":"10.1016/j.apnum.2025.02.011","url":null,"abstract":"<div><div>The Biot model is a coupling problem between the elastic media material with small deformation and porous media fluid flow, its mixed formulation uses the pore pressure, fluid flux, displacement as well as total stress tensor as the primary unknown variables. In this article, combining the discontinuous Galerkin method and the backward Euler method, we propose a mixed discontinuous Galerkin (MDG) method for the mixed Biot equations, it is based on coupling two MDG methods for each subproblem: the MDG method for the porous media fluid flow subproblem and the Hellinger-Reissner formulation of linear elastic subproblem. Then, we prove the well-posedness and the optimal priori error estimates for the MDG method under suitable norms. In particular, the optimal convergence rate of the pressure, displacement and stress tensor in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm and the fluid flux in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm are proved when the storage coefficient <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is strictly positive. Similarly, we deduce the optimal convergence rate of all variables in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm when <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is nonnegative. Finally, some numerical experiments are given to examine the convergence analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 283-299"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454013","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