Pub Date : 2023-11-01DOI: 10.4208/jcm.2303-m2022-0201
Ines Adouani and Chafik Samir
{"title":"Bézier Splines Interpolation on Stiefel and Grassmann Manifolds","authors":"Ines Adouani and Chafik Samir","doi":"10.4208/jcm.2303-m2022-0201","DOIUrl":"https://doi.org/10.4208/jcm.2303-m2022-0201","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139293201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2306-m2022-0279
Hongzheng Ruan and Wei Hong Yang
{"title":"Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information","authors":"Hongzheng Ruan and Wei Hong Yang","doi":"10.4208/jcm.2306-m2022-0279","DOIUrl":"https://doi.org/10.4208/jcm.2306-m2022-0279","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"188 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139299025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2021-0330
Minqiang Xu, Yan-peng Yuan, Waixiang Cao and Qingsong Zou
{"title":"Analysis of Two Any Order Spectral Volume Methods for 1-D Linear Hyperbolic Equations with Degenerate Variable Coefficients","authors":"Minqiang Xu, Yan-peng Yuan, Waixiang Cao and Qingsong Zou","doi":"10.4208/jcm.2305-m2021-0330","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2021-0330","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"92 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139299067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2022-0171
Li Feng and Zhongyi Huang
{"title":"A Uniform Convergent Petrov-Galerkin Method for a Class of Turning Point Problems","authors":"Li Feng and Zhongyi Huang","doi":"10.4208/jcm.2305-m2022-0171","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2022-0171","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"72 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135220890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2302-m2022-0111
Fujun Cao, Dongxu Jia, Dongfang Yuan and Guangwei Yuan
In this paper two dimensional elliptic interface problem with imperfect contact is considered, which is featured by the implicit jump condition imposed on the imperfect contact interface, and the jumping quantity of the unknown is related to the flux across the interface. A finite difference method is constructed for the 2D elliptic interface problems with straight and curve interface shapes. Then, the stability and convergence analysis are given for the constructed scheme. Further, in particular case, it is proved to be monotone. Numerical examples for elliptic interface problems with straight and curve interface shapes are tested to verify the performance of the scheme. The numerical results demonstrate that it obtains approximately second-order accuracy for elliptic interface equations with implicit jump condition.
{"title":"A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact","authors":"Fujun Cao, Dongxu Jia, Dongfang Yuan and Guangwei Yuan","doi":"10.4208/jcm.2302-m2022-0111","DOIUrl":"https://doi.org/10.4208/jcm.2302-m2022-0111","url":null,"abstract":"In this paper two dimensional elliptic interface problem with imperfect contact is considered, which is featured by the implicit jump condition imposed on the imperfect contact interface, and the jumping quantity of the unknown is related to the flux across the interface. A finite difference method is constructed for the 2D elliptic interface problems with straight and curve interface shapes. Then, the stability and convergence analysis are given for the constructed scheme. Further, in particular case, it is proved to be monotone. Numerical examples for elliptic interface problems with straight and curve interface shapes are tested to verify the performance of the scheme. The numerical results demonstrate that it obtains approximately second-order accuracy for elliptic interface equations with implicit jump condition.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"31 11-12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135272647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2022-0215
Pratibha Shakya
{"title":"Error Analysis for Parabolic Optimal Control Problems with Measure Data in a Nonconvex Polygonal Domain","authors":"Pratibha Shakya","doi":"10.4208/jcm.2305-m2022-0215","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2022-0215","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2304-m2022-0185
Jianliang Li, Xiaoli Liu, Bo Zhang and Haiwen Zhang
{"title":"The Nyström Method for Elastic Wave Scattering By Unbounded Rough Surfaces","authors":"Jianliang Li, Xiaoli Liu, Bo Zhang and Haiwen Zhang","doi":"10.4208/jcm.2304-m2022-0185","DOIUrl":"https://doi.org/10.4208/jcm.2304-m2022-0185","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139294940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2305-m2021-0107
Jianchao Bai, Ke Guo, Junli Liang, Yang Jing and H.C. So
{"title":"Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing","authors":"Jianchao Bai, Ke Guo, Junli Liang, Yang Jing and H.C. So","doi":"10.4208/jcm.2305-m2021-0107","DOIUrl":"https://doi.org/10.4208/jcm.2305-m2021-0107","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139301946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.4208/jcm.2304-m2022-0140
Minghua Chen, Fan Yu, Qingdong Zhang and Zhimin Zhang
In this work, we analyze the three-step backward differentiation formula (BDF3) method for solving the Allen-Cahn equation on variable grids. For BDF2 method, the discrete orthogonal convolution (DOC) kernels are positive, the stability and convergence analysis are well established in [Liao and Zhang, newblock Math. Comp., textbf{90} (2021) 1207--1226; Chen, Yu, and Zhang, newblock SIAM J. Numer. Anal., Major Revised]. However, the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial, since the DOC kernels are not always positive. By developing a novel spectral norm inequality, the unconditional stability and convergence are rigorously proved under the updated step ratio restriction $r_k:=tau_k/tau_{k-1}leq 1.405$ (compared with $r_kleq 1.199$ in [Calvo and Grigorieff, newblock BIT. textbf{42} (2002) 689--701]) for BDF3 method. Finally, numerical experiments are performed to illustrate the theoretical results. To the best of our knowledge, this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.
{"title":"Variable Step-Size BDF3 Method for Allen-Cahn Equation","authors":"Minghua Chen, Fan Yu, Qingdong Zhang and Zhimin Zhang","doi":"10.4208/jcm.2304-m2022-0140","DOIUrl":"https://doi.org/10.4208/jcm.2304-m2022-0140","url":null,"abstract":"In this work, we analyze the three-step backward differentiation formula (BDF3) method for solving the Allen-Cahn equation on variable grids. For BDF2 method, the discrete orthogonal convolution (DOC) kernels are positive, the stability and convergence analysis are well established in [Liao and Zhang, newblock Math. Comp., textbf{90} (2021) 1207--1226; Chen, Yu, and Zhang, newblock SIAM J. Numer. Anal., Major Revised]. However, the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial, since the DOC kernels are not always positive. By developing a novel spectral norm inequality, the unconditional stability and convergence are rigorously proved under the updated step ratio restriction $r_k:=tau_k/tau_{k-1}leq 1.405$ (compared with $r_kleq 1.199$ in [Calvo and Grigorieff, newblock BIT. textbf{42} (2002) 689--701]) for BDF3 method. Finally, numerical experiments are performed to illustrate the theoretical results. To the best of our knowledge, this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"17 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135714975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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