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A novel projection-based method for monotone equations with Aitken Δ2 acceleration and its application to sparse signal restoration
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
{"title":"A novel projection-based method for monotone equations with Aitken Δ2 acceleration and its application to sparse signal restoration","authors":"Ahmad Kamandi","doi":"10.1016/j.apnum.2025.02.013","DOIUrl":"10.1016/j.apnum.2025.02.013","url":null,"abstract":"<div><div>In this paper, a novel projection method for solving systems of monotone equations is introduced. The method, employs a search direction based on the normalized negative residual and incorporates a suitable linesearch technique to determine the step length. An accelerated variant is also developed using a vector generalization of the Aitken <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> method, enhanced with a convergence safeguard. These methods are both derivative-free and computationally inexpensive, making them suitable for large-scale problems. The global convergence of these methods is established under specific conditions, and their superior efficiency is demonstrated through numerical tests on large-scale test problems, outperforming several recent accelerated algorithms. Finally, the application of these methods to the signal restoration problem is also discussed.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 1-11"},"PeriodicalIF":2.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487493","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
Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations
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
{"title":"Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations","authors":"Chenxing Li ,&nbsp;Fuzheng Gao ,&nbsp;Jintao Cui","doi":"10.1016/j.apnum.2025.02.015","DOIUrl":"10.1016/j.apnum.2025.02.015","url":null,"abstract":"<div><div>In this paper, we propose a fully discrete implicit method for parabolic problem. The variable-time-step BDF2 method is applied in time combining with the weak Galerkin finite element method in space. Optimal error estimates of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm are derived under the time-step ratio <span><math><mn>0</mn><mo>&lt;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>⩽</mo><mn>4.8645</mn></math></span>. Numerical experiments confirm the theoretical findings. Furthermore, an adaptive scheme is introduced and validated to enhance the computational performance.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 333-343"},"PeriodicalIF":2.2,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488009","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 decoupled nonconforming finite element method for biharmonic equation in three dimensions
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
{"title":"A decoupled nonconforming finite element method for biharmonic equation in three dimensions","authors":"Xuewei Cui,&nbsp;Xuehai Huang","doi":"10.1016/j.apnum.2025.02.012","DOIUrl":"10.1016/j.apnum.2025.02.012","url":null,"abstract":"<div><div>This study focuses on a low-order decoupled nonconforming finite element method for solving the three-dimensional biharmonic equation. The main contribution is to discretize the generalized Stokes equation using a low-order nonconforming element for the <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> space and the lowest order edge element for the pressure. Additionally, the method employs the Lagrange element to solve the Poisson equations. To validate the theoretical convergence rates, numerical experiments are conducted.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 300-311"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454014","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 mixed discontinuous Galerkin method for the Biot equations
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
An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.009
Yande Xia , Yun-Bo Yang
{"title":"An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system","authors":"Yande Xia ,&nbsp;Yun-Bo Yang","doi":"10.1016/j.apnum.2025.02.009","DOIUrl":"10.1016/j.apnum.2025.02.009","url":null,"abstract":"<div><div>In this paper, we propose and analyze a two-grid algorithm based on Newton iteration for solving the stationary inductionless magnetohydrodynamic system. The method involves first solving a small nonlinear system on a coarse grid with grid size <em>H</em>, followed by solving two linear problems on a fine grid with grid size <em>h</em>. These linear problems share the same stiffness matrix but differ only in their right-hand sides. The scaling between the coarse and fine grids is improved by our new method, while the approximate solution retains the same order of convergence as that observed in conventional methods. Furthermore, <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mrow><mi>div</mi></mrow><mo>,</mo><mi>Ω</mi><mo>)</mo><mo>×</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>-conforming finite element pairs are utilized to discretize the current density and electric potential, ensuring that the discrete current density is exactly divergence-free. Stability and convergence analyses are rigorously derived, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error estimates for the velocity are provided. Numerical experiments are presented to verify the theoretical predictions and demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 312-332"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480232","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
Functional equation arising in behavioral sciences: solvability and collocation scheme in Hölder spaces
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.apnum.2025.02.010
Josefa Caballero , Hanna Okrasińska-Płociniczak , Łukasz Płociniczak , Kishin Sadarangani
{"title":"Functional equation arising in behavioral sciences: solvability and collocation scheme in Hölder spaces","authors":"Josefa Caballero ,&nbsp;Hanna Okrasińska-Płociniczak ,&nbsp;Łukasz Płociniczak ,&nbsp;Kishin Sadarangani","doi":"10.1016/j.apnum.2025.02.010","DOIUrl":"10.1016/j.apnum.2025.02.010","url":null,"abstract":"<div><div>We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed arguments. This makes the equation contain two terms with vanishing delays. We prove the existence and uniqueness of the solution in the Hölder space which is a natural function space to consider. In the second part of the paper, we devise an efficient numerical collocation method used to find an approximation to the main problem. We prove the convergence of the scheme and, in passing, several properties of the linear interpolation operator acting on the Hölder space. Numerical simulations verify that the order of convergence of the method (measured in the supremum norm) is equal to the order of Hölder continuity.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 268-282"},"PeriodicalIF":2.2,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446103","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
Estimating the growth of solutions of linear delayed difference and differential equations by alternating maximization
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-17 DOI: 10.1016/j.apnum.2025.02.008
Miloud Sadkane , Roger B. Sidje
{"title":"Estimating the growth of solutions of linear delayed difference and differential equations by alternating maximization","authors":"Miloud Sadkane ,&nbsp;Roger B. Sidje","doi":"10.1016/j.apnum.2025.02.008","DOIUrl":"10.1016/j.apnum.2025.02.008","url":null,"abstract":"<div><div>Numerical methods are proposed to quantify the magnitude of the growth reachable by solutions of systems of delayed linear difference and differential equations that are assumed to be asymptotically stable. A foundation based on an alternating maximization algorithm is established to address the discrete-time case. Following that, it is shown how to reuse this foundation for the continuous-time case, by converting to the discrete-time case through an approximation scheme that uses a backward differentiation formula (BDF) to produce a discretization in time. This indirect conversion approach raises new theoretical questions that are examined thoroughly. The proposed methods apply to systems with constant or variable coefficients. Numerical experiments are included to demonstrate their performance and reliability on several examples.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 254-267"},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427575","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 inverse problem of Robin coefficient identification in parabolic equations with interior degeneracy from terminal observation data
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-13 DOI: 10.1016/j.apnum.2025.02.007
H. Ould Sidi , A.S. Hendy , M.M. Babatin , L. Qiao , M.A. Zaky
{"title":"An inverse problem of Robin coefficient identification in parabolic equations with interior degeneracy from terminal observation data","authors":"H. Ould Sidi ,&nbsp;A.S. Hendy ,&nbsp;M.M. Babatin ,&nbsp;L. Qiao ,&nbsp;M.A. Zaky","doi":"10.1016/j.apnum.2025.02.007","DOIUrl":"10.1016/j.apnum.2025.02.007","url":null,"abstract":"<div><div>In this work, we determine the unknown Robin coefficient in a degenerate parabolic equation. In inverse analysis, the problem under consideration is nonlinear with an ill-formulated operator and nonlocal. For the stable identification of the unknown Robin coefficient, the inverse problem is formulated into a regularised optimization problem. We discuss a variety of practical challenges associated with the problem. The finite element approximation is used to discretize the continuous optimization problem. The convergence and stability analyses are also discussed. Morozov's discrepancy principle is used with the conjugate gradient procedure to construct an iterative scheme. Finally, experiment results are reported to demonstrate the efficiency of the proposed schemes.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 242-253"},"PeriodicalIF":2.2,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422494","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
Two fourth-order conservative compact difference schemes for the generalized Korteweg–de Vries–Benjamin Bona Mahony equation
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-12 DOI: 10.1016/j.apnum.2025.02.005
Xin Zhang , Yuanfeng Jin
{"title":"Two fourth-order conservative compact difference schemes for the generalized Korteweg–de Vries–Benjamin Bona Mahony equation","authors":"Xin Zhang ,&nbsp;Yuanfeng Jin","doi":"10.1016/j.apnum.2025.02.005","DOIUrl":"10.1016/j.apnum.2025.02.005","url":null,"abstract":"<div><div>In this paper, the generalized Korteweg-de Vries–Benjamin Bona Mahony (GKdV-BBM) equation is investigated by two compact finite difference methods. One is a two-level-nonlinear difference scheme and another is a three-level-linearized difference scheme. Both of the schemes provide second and fourth-order accuracy in time and space, respectively. It is important that they preserve certain properties of the original equation, such as conservative properties. The solvability of the proposed numerical schemes is proved by Brouwer's fixed point theorem and mathematical induction, respectively. The unconditional convergence of the proposed difference schemes are also established through the discrete energy method, without imposing any restrictions on the grid ratios. Finally, numerical results are presented to confirm the theoretical findings, and they also demonstrate the efficiency and reliability of the proposed compact approaches.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 223-241"},"PeriodicalIF":2.2,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422493","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
Modified partially randomized extended Kaczmarz method with residual for solving large sparse linear systems
IF 2.2 2区 数学
Applied Numerical Mathematics Pub Date : 2025-02-11 DOI: 10.1016/j.apnum.2025.02.004
Chen-Xiao Gao, Fang Chen
{"title":"Modified partially randomized extended Kaczmarz method with residual for solving large sparse linear systems","authors":"Chen-Xiao Gao,&nbsp;Fang Chen","doi":"10.1016/j.apnum.2025.02.004","DOIUrl":"10.1016/j.apnum.2025.02.004","url":null,"abstract":"<div><div>The partially randomized extended Kaczmarz method with residual is effective for solving large sparse linear systems. In this paper, an improved variant of this method is proposed and its expected exponential convergence rate is proved. In addition, numerical results show that this method can preform better than the partially randomized extended Kaczmarz method with residual.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 215-222"},"PeriodicalIF":2.2,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143422492","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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