Applied Numerical Mathematics最新文献

A unified space-time finite element scheme for a quasilinear parabolic problem

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.apnum.2025.03.006

I. Toulopoulos

引用次数: 0

A revised MRMIL Riemannian conjugate gradient method with simplified global convergence properties

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.apnum.2025.03.007

Nasiru Salihu , Poom Kumam , Sani Salisu , Lin Wang , Kanokwan Sitthithakerngkiet

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On the unconditional long-time L2-stability of the BDF2 time stepping scheme for the two-dimensional Navier-Stokes equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.apnum.2025.03.008

Ming-Cheng Shiue

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A convergent and stable fourth-order iterative procedure based on Kung-Traub conjecture for nonlinear systems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-03-28 DOI: 10.1016/j.apnum.2025.03.003

Asifa Tassaddiq , Sania Qureshi , Ioannis K. Argyros , Francisco I. Chicharro , Amanullah Soomro , Paras Nizamani , Evren Hincal

{"title":"A convergent and stable fourth-order iterative procedure based on Kung-Traub conjecture for nonlinear systems","authors":"Asifa Tassaddiq , Sania Qureshi , Ioannis K. Argyros , Francisco I. Chicharro , Amanullah Soomro , Paras Nizamani , Evren Hincal","doi":"10.1016/j.apnum.2025.03.003","DOIUrl":"10.1016/j.apnum.2025.03.003","url":null,"abstract":"<div><div>Iterative algorithms are essential in computer research because they solve nonlinear models. This study presents a new and efficient approach for finding the roots of nonlinear equations and nonlinear systems of equations. The algorithm follows a two-step process and aims to optimize the iterative process. Based on Kung-Traub conjecture, the method shows optimal convergence and only needs three function evaluations per iteration. This creates a fourth-order optimal iterative procedure with an efficiency index of about 1.5874. This method utilizes a combination of two well-established third-order iterative approaches. The analyses of local and semilocal convergence, as well as stability analysis using complex dynamics, provide substantial improvements compared to current methods. We have extensively tested the proposed algorithm on a range of nonlinear models, including chemical reactions, kinetic synthesis, and non-adiabatic stirred tank reactors, consistently demonstrating accurate and efficient results. In terms of both speed and accuracy, it outperforms contemporary algorithms.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"214 ","pages":"Pages 54-79"},"PeriodicalIF":2.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738307","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

Hamiltonian boundary value methods applied to KdV-KdV systems

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-03-27 DOI: 10.1016/j.apnum.2025.02.006

Qian Luo , Aiguo Xiao , Xuqiong Luo , Xiaoqiang Yan

引用次数: 0

Splitting techniques for DAEs with port-Hamiltonian applications

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-03-26 DOI: 10.1016/j.apnum.2025.03.004

Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther , Nicole Marheineke

{"title":"Splitting techniques for DAEs with port-Hamiltonian applications","authors":"Andreas Bartel , Malak Diab , Andreas Frommer , Michael Günther , Nicole Marheineke","doi":"10.1016/j.apnum.2025.03.004","DOIUrl":"10.1016/j.apnum.2025.03.004","url":null,"abstract":"<div><div>In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints. This paper focuses on operator splitting techniques for coupled systems and aims at preserving the structure in the port-Hamiltonian framework. The study explores two decomposition strategies: one considering the underlying coupled subsystem structure and the other addressing energy-associated properties such as conservation and dissipation. We show that for coupled index-1 DAEs with and without private index-2 variables, the splitting schemes on top of a dimension-reducing decomposition achieve the same convergence rate as in the case of ordinary differential equations. Additionally, we discuss an energy-associated decomposition for linear time-invariant port-Hamiltonian index-1 DAEs and introduce generalized Cayley transforms to uphold energy conservation. The effectiveness of both strategies is evaluated using port-Hamiltonian benchmark examples from electric circuits.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"214 ","pages":"Pages 28-53"},"PeriodicalIF":2.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Finite block method for nonlinear time-fractional partial integro-differential equations: Stability, convergence, and numerical analysis

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

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

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

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