发布求助
文献互助 智能选刊 最新文献

Results in Applied Mathematics最新文献

筛选
英文 中文
Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation 结合BDF2-θ的两网格混合有限元法求解二维非线性分数阶伪双曲型波动方程
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100530
Yan Wang, Yining Yang, Nian Wang, Hong Li, Yang Liu
{"title":"Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation","authors":"Yan Wang,&nbsp;Yining Yang,&nbsp;Nian Wang,&nbsp;Hong Li,&nbsp;Yang Liu","doi":"10.1016/j.rinam.2024.100530","DOIUrl":"10.1016/j.rinam.2024.100530","url":null,"abstract":"<div><div>In this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter <span><math><mi>θ</mi></math></span> is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD) formula is used to approximate the fractional time derivative at time <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>θ</mi></mrow></msub></math></span>, and the spatial direction is approximated by a two-grid <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Galerkin MFE method. The error estimates in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm for the fully discrete T-GMFE system are proved. Further, a modified T-GMFE scheme is proposed and the optimal error results are provided. Finally, computing results show the presented T-GMFE method can save computing time and improve the computational efficiency.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100530"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints 具有点向控制约束的椭圆型Neumann边界控制问题的有限元误差分析
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100544
Susanne C. Brenner, Li-Yeng Sung
{"title":"A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints","authors":"Susanne C. Brenner,&nbsp;Li-Yeng Sung","doi":"10.1016/j.rinam.2025.100544","DOIUrl":"10.1016/j.rinam.2025.100544","url":null,"abstract":"<div><div>We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficients in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100544"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fully decoupled SAV Fourier-spectral scheme for the Cahn–Hilliard–Hele–Shaw system Cahn-Hilliard-Hele-Shaw系统的完全解耦SAV傅立叶谱格式
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100534
Linhui Zhang , Hongen Jia , Hongbin Wang
{"title":"Fully decoupled SAV Fourier-spectral scheme for the Cahn–Hilliard–Hele–Shaw system","authors":"Linhui Zhang ,&nbsp;Hongen Jia ,&nbsp;Hongbin Wang","doi":"10.1016/j.rinam.2024.100534","DOIUrl":"10.1016/j.rinam.2024.100534","url":null,"abstract":"<div><div>In this paper, we construct first- and second-order fully discrete schemes for the Cahn–Hilliard–Hele–Shaw system based on the Fourier-spectral method for spatial discretization. For temporal discretization, we combine two efficient approaches, including the scalar auxiliary variable (SAV) method for linearizing nonlinear potentials and the zero-energy-contribution method (ZEC) for decoupling nonlinear couplings. These schemes are linear, fully decoupled, and unconditionally energy stable, requiring only the solution of a sequence of elliptic equations with constant coefficients at each time step. The rigorous proof of the error analysis for the first-order scheme is shown. In addition, several numerical examples are presented to demonstrate the stability, accuracy, and efficiency of the proposed scheme.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100534"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structured backward errors for block three-by-three saddle point systems with Hermitian and sparsity block matrices 具有厄米矩阵和稀疏分块矩阵的块3乘3鞍点系统的结构向后误差
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100546
Bing Tan, Wei Ma
{"title":"Structured backward errors for block three-by-three saddle point systems with Hermitian and sparsity block matrices","authors":"Bing Tan,&nbsp;Wei Ma","doi":"10.1016/j.rinam.2025.100546","DOIUrl":"10.1016/j.rinam.2025.100546","url":null,"abstract":"<div><div>In this paper, we explore the structured backward errors for a class of block three-by-three saddle point systems with Hermitian and sparsity block matrices. We derive an explicit formula for the structured backward errors under the assumption that the inherent matrix structure and sparsity pattern are maintained in the associated perturbation. Moreover, the optimal backward perturbation matrix for achieving structured backward error is constructed. Our analysis further explores the structured backward error when the sparsity structure is not preserved. Numerical experiments show that the computable formulas of structured backward errors are useful for testing the stability of practical algorithms.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100546"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PINN based on multi-scale strategy for solving Navier–Stokes equation 基于多尺度策略的 PINN，用于求解纳维-斯托克斯方程
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100526
Shirong Li , Shaoyong Lai
{"title":"PINN based on multi-scale strategy for solving Navier–Stokes equation","authors":"Shirong Li ,&nbsp;Shaoyong Lai","doi":"10.1016/j.rinam.2024.100526","DOIUrl":"10.1016/j.rinam.2024.100526","url":null,"abstract":"<div><div>Neural networks combined with automatic differentiation technology provide a fundamental framework for the numerical solution of partial differential equations. This framework constitutes a loss function driven by both data and physical models, significantly enhancing generalization capabilities. Combining the framework and the idea of multi-scale methods in traditional numerical methods, such as domain decomposition and collocation self-adaption, we construct a method of the Physics-Informed Neural Networks (PINNs) based on multi-scale strategy to solve Navier–Stokes equations, and the results are more effective than XPINNs and SAPINNs. The computational efficiency of the proposed method is verified by solving two-dimensional and three-dimensional Navier–Stokes equations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100526"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fully discrete P02−P1 mixed elements for optimal control with parabolic equations and low regularity 完全离散P02−P1混合单元的最优控制与抛物方程和低正则性
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100551
Yuelong Tang, Yuchun Hua, Yujun Zheng, Chao Wu
{"title":"Fully discrete P02−P1 mixed elements for optimal control with parabolic equations and low regularity","authors":"Yuelong Tang,&nbsp;Yuchun Hua,&nbsp;Yujun Zheng,&nbsp;Chao Wu","doi":"10.1016/j.rinam.2025.100551","DOIUrl":"10.1016/j.rinam.2025.100551","url":null,"abstract":"<div><div>This paper studies a novel fully discrete mixed method for optimal control problems (OCPs) with parabolic equations and low regularity. The backward difference scheme and <span><math><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> mixed finite elements (MFEs) are used for temporal and spatial discretization of state and adjoint state, respectively. Error estimates of all variables are derived through the introduction of specific auxiliary variables and the application of suitable regularity assumptions. The theoretical analysis is validated by two numerical examples.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100551"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FastLRNR and Sparse Physics Informed Backpropagation FastLRNR和稀疏物理通知反向传播
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100547
Woojin Cho , Kookjin Lee , Noseong Park , Donsub Rim , Gerrit Welper
{"title":"FastLRNR and Sparse Physics Informed Backpropagation","authors":"Woojin Cho ,&nbsp;Kookjin Lee ,&nbsp;Noseong Park ,&nbsp;Donsub Rim ,&nbsp;Gerrit Welper","doi":"10.1016/j.rinam.2025.100547","DOIUrl":"10.1016/j.rinam.2025.100547","url":null,"abstract":"<div><div>We introduce <u>S</u>parse <u>P</u>hysics <u>In</u>formed Back<u>prop</u>agation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR). The approach exploits the low rank structure within LRNR and constructs a reduced neural network approximation that is much smaller in size. We call the smaller network FastLRNR. We show that backpropagation of FastLRNR can be substituted for that of LRNR, enabling a significant reduction in complexity. We apply SPInProp to a physics informed neural networks framework and demonstrate how the solution of parametrized partial differential equations is accelerated.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100547"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of multiple weak solutions to a weighted quasilinear elliptic equation 一类加权拟线性椭圆方程多个弱解的存在性
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100536
Khaled Kefi
{"title":"Existence of multiple weak solutions to a weighted quasilinear elliptic equation","authors":"Khaled Kefi","doi":"10.1016/j.rinam.2024.100536","DOIUrl":"10.1016/j.rinam.2024.100536","url":null,"abstract":"<div><div>In this study, we explore the existence of solutions to certain quasilinear degenerate elliptic equations that involve Hardy singular coefficients. Using variational techniques and critical point theorems, we establish new criteria for the existence of at least three weak solutions, under the assumption that the nonlinearity meets appropriate conditions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100536"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 numerical solution of an Abel integral equation by the optimal quadrature formula 用最优正交公式求解阿贝尔积分方程的数值解
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100542
Abdullo Hayotov , Samandar Babaev , Bobomurod Boytillayev
{"title":"The numerical solution of an Abel integral equation by the optimal quadrature formula","authors":"Abdullo Hayotov ,&nbsp;Samandar Babaev ,&nbsp;Bobomurod Boytillayev","doi":"10.1016/j.rinam.2025.100542","DOIUrl":"10.1016/j.rinam.2025.100542","url":null,"abstract":"<div><div>In this study, a novel and efficient approach utilizing optimal quadrature formulas is introduced to derive approximate solutions for generalizing Abel’s integral equations. The method, characterized by high accuracy and simplicity, involves constructing optimal quadrature formulas in the sense of Sard and providing error estimates within the Hilbert space of differentiable functions. The squared norm of the error functional for the quadrature formula in the space <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> is computed. To minimize this error, a system of linear equations regarding the formula’s coefficients is derived, leading to a unique solution. Then the explicit expressions for these optimal coefficients are obtained. The validity of the approach is demonstrated by solving several integral equations, with approximation errors presented in the corresponding tables.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100542"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two step inertial Tseng method for solving monotone variational inclusion problem 求解单调变分包含问题的两步惯性Tseng法
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100545
Lehlogonolo Mokaba , Hammed Anuoluwapo Abass , Abubakar Adamu
{"title":"Two step inertial Tseng method for solving monotone variational inclusion problem","authors":"Lehlogonolo Mokaba ,&nbsp;Hammed Anuoluwapo Abass ,&nbsp;Abubakar Adamu","doi":"10.1016/j.rinam.2025.100545","DOIUrl":"10.1016/j.rinam.2025.100545","url":null,"abstract":"<div><div>In this paper, we examine the monotone variational inclusion problem with a maximal monotone operator and a Lipschitz continuous monotone operator. We propose two different iterative algorithms for solving the monotone variational inclusion problem, utilizing a new self-adaptive step size and a two-step inertial technique. Under the assumption that the solution set of the monotone variational inclusion problem is nonempty, we prove weak and strong convergence theorems concerning the sequences generated by our proposed algorithms. The convergence is guaranteed under some mild assumptions. Some numerical experiments are presented to demonstrate the performance of our iterative algorithms in comparison with recent results in the literature.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100545"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信