Applied Numerical Mathematics最新文献_第4页

A higher-order solver for the FitzHugh-Nagumo equation by combining nonstandard and compact finite difference scheme 结合非标准与紧致有限差分格式求解FitzHugh-Nagumo方程的高阶解

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-09 DOI: 10.1016/j.apnum.2025.07.004

Zhi-Chen Li , Yang-Wen Yu , Xiao-Yu Zhang , Qing Fang

引用次数: 0

High-level convergence order accelerators of iterative methods for nonlinear problems 非线性问题迭代法的高收敛阶加速器

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-08 DOI: 10.1016/j.apnum.2025.07.003

Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva

引用次数: 0

Low-storage exponentially fitted explicit Runge-Kutta methods 低存储指数拟合显式龙格-库塔方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-05 DOI: 10.1016/j.apnum.2025.06.017

I. Higueras , J.I. Montijano , L. Rández

{"title":"Low-storage exponentially fitted explicit Runge-Kutta methods","authors":"I. Higueras , J.I. Montijano , L. Rández","doi":"10.1016/j.apnum.2025.06.017","DOIUrl":"10.1016/j.apnum.2025.06.017","url":null,"abstract":"<div><div>In this paper, we study explicit Runge-Kutta (RK) methods for solving high-dimensional systems of ordinary differential equations (ODEs), with oscillatory or periodic solutions, that can be implemented with a few memory registers. We will refer to these schemes as Low-Storage Exponentially Fitted explicit Runge-Kutta methods (LSEFRK).</div><div>In order to obtain them, we first study second-order and third-order low-storage (LS) schemes that can be implemented with two memory registers per step of the van der Houwen- and Williamson-type. Next, we construct optimal LSEFRK methods by imposing exponential fitting conditions along with accuracy and stability properties. In this way, new optimal three-stage third-order and five-stage fourth-order LSEFRK schemes are constructed for each type of LS method.</div><div>The performance of these new schemes is tested by solving some high-dimensional differential systems with periodic solutions. Comparison with other non-LS exponentially fitted and low-storage non-EF RK methods from the literature shows that the new LSEFRK schemes outperform the efficiency of RK methods that only satisfy either the LS or the EF condition.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 372-389"},"PeriodicalIF":2.2,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580372","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

High-order structure-preserving approaches for constrained conservative or dissipative systems 约束保守或耗散系统的高阶结构保持方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-05 DOI: 10.1016/j.apnum.2025.06.018

Jiaxiang Cai , Yushun Wang

引用次数: 0

Piecewise logarithmic Chebyshev cardinal functions: Application for nonlinear integral equations with a logarithmic singular kernel 分段对数切比雪夫基数函数：具有对数奇异核的非线性积分方程的应用

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-04 DOI: 10.1016/j.apnum.2025.06.016

M.H. Heydari , D. Baleanu , M. Bayram

{"title":"Piecewise logarithmic Chebyshev cardinal functions: Application for nonlinear integral equations with a logarithmic singular kernel","authors":"M.H. Heydari , D. Baleanu , M. Bayram","doi":"10.1016/j.apnum.2025.06.016","DOIUrl":"10.1016/j.apnum.2025.06.016","url":null,"abstract":"<div><div>This study introduces a novel class of nonlinear integral equations with a logarithmic singular kernel. The existence and uniqueness of a solution to these equations are rigorously analyzed. To facilitate their solution, we construct the piecewise logarithmic Chebyshev cardinal functions (CCFs), a versatile family of basis functions. In this framework, an operational matrix for the Hadamard fractional integral is derived for the PLCCFs. By employing the connection between this type of logarithmic singularity and the Hadamard fractional integral operator, we develop a straightforward yet powerful numerical approach to solve these equations. In the proposed method, the solution is first approximated using a finite expansion of the piecewise logarithmic CCFs with unknown coefficients. Then, through interpolation and the application of the fractional integral operational matrix, the original integral equation is reformulated as a system of nonlinear algebraic equations, whose solution determines the expansion coefficients. The convergence analysis of the proposed scheme is examined through both theoretical and numerical investigations. The accuracy of the developed method is evaluated by solving some illustrative examples featuring both analytical and non-analytical solutions.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 355-371"},"PeriodicalIF":2.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144570254","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

Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media 随机非均质多孔介质中源型流动不确定性量化的代数多重网格方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-07-03 DOI: 10.1016/j.apnum.2025.06.015

Vincenzo Schiano Di Cola , Salvatore Cuomo , Gerardo Severino , Marco Berardi

引用次数: 0

A surface mesh DG-VEM for elliptic membrane shell model 椭圆膜壳模型的表面网格DG-VEM

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-30 DOI: 10.1016/j.apnum.2025.06.014

Qian Yang , Xiaoqin Shen , Jikun Zhao , Zhiming Gao

{"title":"A surface mesh DG-VEM for elliptic membrane shell model","authors":"Qian Yang , Xiaoqin Shen , Jikun Zhao , Zhiming Gao","doi":"10.1016/j.apnum.2025.06.014","DOIUrl":"10.1016/j.apnum.2025.06.014","url":null,"abstract":"<div><div>Elliptic membrane shell (EMS), characterized by a system with complex variable coefficients on a surface, poses significant challenges for numerical discretization. In this paper, leveraging the differing regularity of displacement components, we propose a discontinuous Galerkin virtual element method (DG-VEM) for the EMS model. Specifically, we construct <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-continuous virtual element spaces for the first two components, whereas the third component is discretized on each element using a polynomial of degree <em>l</em>, with no continuity enforced across element boundaries. This method offers high mesh flexibility, eliminates the need for explicit basis function expressions, and improves accuracy to achieve convergence of any desired order. Furthermore, we establish the existence, uniqueness, stability, and convergence of the numerical solution, along with rigorous error estimates. Several numerical examples are presented to test the convergence and stability of the DG-VEM. Additionally, we demonstrate the method's adaptability to diverse grid subdivisions and show that, for comparable error levels, the DG-VEM for the EMS model requires significantly fewer degrees of freedom than traditional finite element methods.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 298-318"},"PeriodicalIF":2.2,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517713","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

Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates 线性偏微分方程的指数精度谱蒙特卡罗方法及其误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-26 DOI: 10.1016/j.apnum.2025.06.010

Jiaying Feng, Changtao Sheng, Chenglong Xu

{"title":"Exponentially accurate spectral Monte Carlo method for linear PDEs and their error estimates","authors":"Jiaying Feng, Changtao Sheng, Chenglong Xu","doi":"10.1016/j.apnum.2025.06.010","DOIUrl":"10.1016/j.apnum.2025.06.010","url":null,"abstract":"<div><div>This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by <em>α</em>-stable Lévy processes with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, which was initially proposed and developed by Gobet and Maire in their pioneering works ((2004) <span><span>[24]</span></span>, and (2005) <span><span>[25]</span></span>) for the case <span><math><mi>α</mi><mo>=</mo><mn>2</mn></math></span>. The novel method effectively integrates multiple computational techniques, including the interpolation based on generalized Jacobi functions (GJFs), space-time spectral methods, control variates techniques, and a novel walk-on-spheres method (WOS). The exponential convergence of the error bounds is rigorously established through finite iterations for both Poisson and parabolic equations involving the integral fractional Laplacian operator. Remarkably, the proposed space-time spectral Monte Carlo method (ST-SMC) for the parabolic equation is unified for both <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>α</mi><mo>=</mo><mn>2</mn></math></span>. Extensive numerical results are provided to demonstrate the spectral accuracy and efficiency of the proposed method, thereby validating the theoretical findings.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 278-297"},"PeriodicalIF":2.2,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489532","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

Generalization error analysis of deep backward dynamic programming for solving nonlinear PDEs 求解非线性偏微分方程的深度后向动态规划泛化误差分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-26 DOI: 10.1016/j.apnum.2025.06.013

Du Ouyang, Jichang Xiao, Xiaoqun Wang

{"title":"Generalization error analysis of deep backward dynamic programming for solving nonlinear PDEs","authors":"Du Ouyang, Jichang Xiao, Xiaoqun Wang","doi":"10.1016/j.apnum.2025.06.013","DOIUrl":"10.1016/j.apnum.2025.06.013","url":null,"abstract":"<div><div>We explore the application of the quasi-Monte Carlo (QMC) method in deep backward dynamic programming (DBDP) <span><span>[1]</span></span> for numerically solving high-dimensional nonlinear partial differential equations (PDEs). Our study focuses on examining the generalization error as a component of the total error in the DBDP framework, discovering that the rate of convergence for the generalization error is influenced by the choice of sampling methods. Specifically, for a given batch size <em>m</em>, the generalization error under QMC methods exhibits a convergence rate of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>+</mo><mi>ε</mi></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> can be made arbitrarily small. This rate is notably more favorable than that of the traditional Monte Carlo (MC) methods, which is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>ε</mi></mrow></msup><mo>)</mo></math></span>. Our theoretical analysis shows that the generalization error under QMC methods achieves a higher order of convergence than their MC counterparts. Numerical experiments demonstrate that QMC indeed surpasses MC in delivering solutions that are both more precise and stable.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 319-339"},"PeriodicalIF":2.2,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522669","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 method and analysis for fluid-structure model on unbounded domains 无界域流固模型的数值方法与分析

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-06-25 DOI: 10.1016/j.apnum.2025.06.009

Hongwei Li, Xinyue Chen

{"title":"Numerical method and analysis for fluid-structure model on unbounded domains","authors":"Hongwei Li, Xinyue Chen","doi":"10.1016/j.apnum.2025.06.009","DOIUrl":"10.1016/j.apnum.2025.06.009","url":null,"abstract":"<div><div>Numerically solving the fluid-structure model on unbounded domains poses a challenge, due to the unbounded nature of the physical domain. To overcome this challenge, the artificial boundary method is specifically applied to numerically solve the fluid-structure model on unbounded domains, which can be used to analyze fluid-structure interactions in various scientific and engineering fields. Drawing inspiration from the artificial boundary method, we employ artificial boundaries to truncate the unbounded domain, subsequently designing the high order local artificial boundary conditions thereon based on the Padé approximation. Then, the initial value problem on the unbounded domain is reduced into an initial boundary value problem on the computational domain, which can be efficiently solved by adopting the finite difference method. Furthermore, a series of auxiliary variables is introduced specifically to address the issue of mixed derivatives arising in the artificial boundary conditions, and the stability, convergence and solvability of the reduced problem are rigorously analyzed. Numerical experiments are reported to demonstrate the effectiveness of artificial boundary conditions and theoretical analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"217 ","pages":"Pages 255-277"},"PeriodicalIF":2.2,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489531","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