Applied Numerical Mathematics最新文献_第9页

A Multi-Quadrics quasi-interpolation scheme for numerical solution of Burgers' equation

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.025

JiHong Zhang, JiaLi Yu

引用次数: 0

On an algorithm for the numerical solution of quasilinear integral-algebraic equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.10.008

Mikhail Bulatov , Tatiana Indutskaya , Liubov Solovarova

引用次数: 0

Numerical differentiation of the piecewise smooth function by using Fourier extension method

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.09.026

Zhenyu Zhao , Kai Yu , Xianzheng Jia , Zhihong Dou

引用次数: 0

An explicit substructuring method for overlapping domain decomposition based on stochastic calculus 基于随机微积分的重叠域分解显式子结构方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.apnum.2024.02.011

Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki

{"title":"An explicit substructuring method for overlapping domain decomposition based on stochastic calculus","authors":"Jorge Morón-Vidal, Francisco Bernal, Atsushi Suzuki","doi":"10.1016/j.apnum.2024.02.011","DOIUrl":"10.1016/j.apnum.2024.02.011","url":null,"abstract":"<div><div>In a recent paper <span><span>[7]</span></span>, a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton, the hybrid approach produces an explicit and sparse shrunken matrix—hence suitable for substructuring again. The ultimate goal is to push strong scalability beyond the state of the art by leveraging the potential for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and—crucially—for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler, and more accurate while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"208 ","pages":"Pages 340-355"},"PeriodicalIF":2.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956478","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

The Crank-Nicolson weak Galerkin finite element methods for the sine-Gordon equation 正弦-戈登方程的Crank-Nicolson弱Galerkin有限元方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-29 DOI: 10.1016/j.apnum.2025.01.016

Ahmed Al-Taweel , Jumana Alkhalissi , Xiaoshen Wang

引用次数: 0

Spectral element method for the solution of viscoelastic seismic wave propagation 黏弹性地震波传播的谱元解法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-27 DOI: 10.1016/j.apnum.2025.01.015

Feze Barzegar, Jalil Rashidinia

引用次数: 0

Error estimates of implicit-explicit compact BDF2 schemes for the pseudo parabolic equations with logarithmic nonlinearity 对数非线性伪抛物方程隐显紧BDF2格式的误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.apnum.2025.01.010

Qifeng Zhang , Haiyan Cao , Hongyu Qin

引用次数: 0

Energy stability and error estimate of the RKMK2e scheme for the extended Fisher–Kolmogorov equation 扩展Fisher-Kolmogorov方程RKMK2e格式的能量稳定性和误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.apnum.2025.01.014

Haifeng Wang, Yan Wang, Hong Zhang, Songhe Song

引用次数: 0

Refined variational iteration method through optimal linear operator and Lagrange multiplier: Local/global convergence 通过最优线性算子和拉格朗日乘子的改进变分迭代方法：局部/全局收敛

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.apnum.2025.01.013

Tapas Roy, Dilip Kumar Maiti

{"title":"Refined variational iteration method through optimal linear operator and Lagrange multiplier: Local/global convergence","authors":"Tapas Roy, Dilip Kumar Maiti","doi":"10.1016/j.apnum.2025.01.013","DOIUrl":"10.1016/j.apnum.2025.01.013","url":null,"abstract":"<div><div>Our focus is on refining the Variational Iteration Method (VIM), which will henceforth be called R-VIM. We begin by introducing a general linear operator and consequently the Lagrange's multiplier; then, minimizing the residual error, we subsequently find the optimal linear operator as well as the best fitting Lagrange's multiplier for a given differential equation. By means of Banach Fixed Point Theorem, the necessary conditions for the convergence of the solutions of VIM, Optimal VIM, and R-VIM are established involving the Lagrange's multiplier; it has been demonstrated (and subsequently numerically certified) that solutions of VIM and Optimal VIM locally converge. While R-VIM solutions, with the aid of necessary and sufficient criteria, have been shown to converge globally for appropriate values of the unknown parameters involved in the general linear operator. We make sure that the convergence of the VIM solution depends critically on the optimal selection of the linear operator and, consequently, the best suited Lagrange's multiplier.</div><div>Our bird's eye view would be to differentiate between the contributions of the homotopy equation in homotopy-based approaches and Lagrange's multiplier-based correction functional of the VIM for the fastest convergence. Furthermore, in order to achieve fast convergence, we additionally examine if the optimal VIM's regulating parameter offers any further benefit above proposed R-VIM. We aim to apply R-VIM to problems with multiple solutions to ensure that all solutions are accurately identified. Our proposed method has been proven superior and more widely applicable through both theoretical and numerical illustrations. However, it also has its limits. Hence, we suggest the implementation of the multistep R-VIM, referred to as MR-VIM, as a means to solve chaotic dynamical systems.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 1-28"},"PeriodicalIF":2.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154831","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 unconditionally stable second-order scheme for Maxwell's equations in the Cole–Cole dispersive medium

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-01-22 DOI: 10.1016/j.apnum.2025.01.009

Jingjing Xiao , Desong Kong

引用次数: 0