Computers & Mathematics with Applications最新文献_第2页

Decoupling technology for systems of evolutionary equations 演化方程系统的解耦技术

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-28 DOI: 10.1016/j.camwa.2025.04.022

P.N. Vabishchevich

{"title":"Decoupling technology for systems of evolutionary equations","authors":"P.N. Vabishchevich","doi":"10.1016/j.camwa.2025.04.022","DOIUrl":"10.1016/j.camwa.2025.04.022","url":null,"abstract":"<div><div>Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a new level in time. The decoupling method, a significant approach to simplifying the problem, is based on the decomposition of the problem's operator matrix. The approximate solution is constructed based on the linear composition of solutions to auxiliary problems. The paper investigates decoupling variants based on extracting the diagonal part of the operator matrix and the lower and upper triangular submatrices. The study introduces a new decomposition approach, which involves splitting the operator matrix into rows and columns. The composition stage utilizes various variants of splitting schemes, showcasing the versatility of the approach. In additive operator-difference schemes, we can distinguish explicit-implicit schemes, factorized schemes for two-component splitting, and regularized schemes for general multi-component splitting. The study of stability of two- and three-level decoupling composition schemes is carried out using the theory of stability (correctness) of operator-difference schemes for finite-dimensional Hilbert spaces. The theoretical results of the decoupling technique for systems of evolution equations are illustrated on a test two-dimensional problem for a coupled system of two diffusion equations with inhomogeneous self- and cross-diffusion coefficients.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"191 ","pages":"Pages 105-128"},"PeriodicalIF":2.9,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882097","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 positive meshless finite difference scheme for scalar conservation laws with adaptive artificial viscosity driven by fault detection 基于故障检测的自适应人工黏度标量守恒律的正无网格有限差分格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-28 DOI: 10.1016/j.camwa.2025.04.006

Cesare Bracco , Oleg Davydov , Carlotta Giannelli , Alessandra Sestini

引用次数: 0

A moving mesh method for pitting corrosion of heterogeneous materials 非均质材料点蚀的移动网格法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-25 DOI: 10.1016/j.camwa.2025.04.005

Abu Naser Sarker , Ronald D. Haynes , Michael Robertson

引用次数: 0

The improved boundary knot method with fictitious points for solving high-order Helmholtz-type PDEs 求解高阶helmholtz型偏微分方程的改进虚点边界结法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-25 DOI: 10.1016/j.camwa.2025.04.017

L. Liu, L.L. Zhang, M. Lei, R.P. Niu

引用次数: 0

Quasi-uniform unconditional superconvergent error estimates of FEMs for the time-dependent singularly perturbed Bi-wave problem modeling d-wave superconductors d波超导体时域奇摄动双波问题fem的准均匀无条件超收敛误差估计

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-24 DOI: 10.1016/j.camwa.2025.04.018

Yanmi Wu , Dongyang Shi

引用次数: 0

A virtual element method for a convective Brinkman-Forchheimer problem coupled with a heat equation 与热方程耦合的对流布林克曼-福克海默问题的虚拟元素法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-23 DOI: 10.1016/j.camwa.2025.04.015

Danilo Amigo , Felipe Lepe , Enrique Otárola , Gonzalo Rivera

引用次数: 0

Analysis of spectral Galerkin method with higher order time discretization for the nonlinear stochastic Fisher's type equation driven by multiplicative noise 乘性噪声驱动下非线性随机Fisher型方程的高阶时间离散化谱伽辽金方法分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-23 DOI: 10.1016/j.camwa.2025.04.016

Huanrong Li , Rushuang Yang

{"title":"Analysis of spectral Galerkin method with higher order time discretization for the nonlinear stochastic Fisher's type equation driven by multiplicative noise","authors":"Huanrong Li , Rushuang Yang","doi":"10.1016/j.camwa.2025.04.016","DOIUrl":"10.1016/j.camwa.2025.04.016","url":null,"abstract":"<div><div>This paper primarily focuses on developing a high-order-in-time spectral Galerkin approximation method for nonlinear stochastic Fisher's type equations driven by multiplicative noise. For this reason, we first design an improved discretization scheme in time based on the Milstein method, and then propose a spectral Galerkin approximation method in space. We analyze the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> stability and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stability estimations for numerical solutions of the proposed fully discrete spectral Galerkin approximation formulation under reasonable assumptions about the multiplicative noise function <span><math><mi>g</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> and the nonlinear multiplicative function <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>)</mo></math></span>. Additionally, we achieve nearly optimal error convergence orders in both space and time. Especially, the time convergence order almost reaches 1 under the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm. Finally, several numerical experiments are carried out for the stochastic Fisher's type models to validate all the theoretical results, and it can also be seen that the numerical results are consistent with the physical properties of the Fisher's equation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"190 ","pages":"Pages 90-102"},"PeriodicalIF":2.9,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143858303","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 difference schemes for nonlinear Riesz space variable-order fractional diffusion equations 非线性Riesz空间变阶分数扩散方程的高阶差分格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-22 DOI: 10.1016/j.camwa.2025.04.010

Qiu-Ya Wang

{"title":"High order difference schemes for nonlinear Riesz space variable-order fractional diffusion equations","authors":"Qiu-Ya Wang","doi":"10.1016/j.camwa.2025.04.010","DOIUrl":"10.1016/j.camwa.2025.04.010","url":null,"abstract":"<div><div>This article aims at studying new finite difference methods for one-dimensional and two-dimensional nonlinear Riesz space variable-order (VO) fractional diffusion equations. In the presented model, fractional derivatives are defined in the Riemann-Liouville type. Based on 4-point weighted-shifted-Grünwald-difference (4WSGD) operators for Riemann-Liouville constant-order fractional derivatives, which have a free parameter and have at least third order accuracy, we derive variable-order 4WSGD operators for space Riesz variable-order fractional derivatives. In order that the fully discrete schemes exhibit robust stability and can handle the nonlinear term efficiently, we employ the implicit Euler (IE) method to discretize the time derivative, which leads to IE-4WSGD schemes. The stability and convergence properties of the IE-4WSGD schemes are analyzed theoretically. Additionally, a parameter selection strategy is derived for 4WSGD schemes and banded preconditioners are put forward to accelerate the GMRES methods for solving the discretization linear systems. Numerical results demonstrate the effectiveness of the proposed IE-4WSGD schemes and preconditioners.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"188 ","pages":"Pages 221-243"},"PeriodicalIF":2.9,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854843","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

Analysis of transient free surface seepage flow using numerical manifold method 瞬态自由地表渗流数值流形分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-17 DOI: 10.1016/j.camwa.2025.04.011

Zhen Jia, Hong Zheng

{"title":"Analysis of transient free surface seepage flow using numerical manifold method","authors":"Zhen Jia, Hong Zheng","doi":"10.1016/j.camwa.2025.04.011","DOIUrl":"10.1016/j.camwa.2025.04.011","url":null,"abstract":"<div><div>In the analysis of transient seepage flow with free surfaces, not only the free surfaces but also the boundary conditions vary with time, introducing significant challenges to those traditional mesh-based numerical methods. Although the numerical manifold method (NMM) has shown great advantages in tracking time-independent free surface seepage flow due to its dual cover systems – the mathematical cover and the physical cover, in the analysis of transient free surface seepage flow it will encounter the inheritance issue of degrees of freedom between two consecutive time steps, which is still an open issue for all the partition of unity based methods such as the extended finite element method (XFEM) and the generalized finite element method (GFEM). It is shown in this study that the issue can be easily overcome if a different discretization order from the classical discretization order is adopted, <em>i.e.</em>, time discretization is carried out before to spatial discretization. By analyzing typical transient seepage examples, the positions of the transient free surfaces predicted by the proposed method are excellently consistent with analytical solutions or experimental results. At the same time, it also points out the errors and possible consequences of some literature concerning the handling of sudden drops in upstream water level. The results demonstrate that the proposed procedure not only effectively predicts the evolution of free surfaces but also accurately addresses transient seepage problems, including those with complex drainage systems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"189 ","pages":"Pages 129-143"},"PeriodicalIF":2.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839089","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 second-order, unconditionally invariant-set-preserving scheme for the FitzHugh-Nagumo equation FitzHugh-Nagumo方程的二阶无条件不变集保持格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-04-17 DOI: 10.1016/j.camwa.2025.04.013

Yiyi Liu , Xueqing Teng , Xiaoqiang Yan , Hong Zhang

引用次数: 0