Pub Date : 2023-09-01DOI: 10.4208/jcm.2302-m2022-0033
Hanzhang Hu, Yanping Chen and Jianwei Zhou
{"title":"Two-Grid Finite Element Method for Time-Fractional Nonlinear Schrödinger Equation","authors":"Hanzhang Hu, Yanping Chen and Jianwei Zhou","doi":"10.4208/jcm.2302-m2022-0033","DOIUrl":"https://doi.org/10.4208/jcm.2302-m2022-0033","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135298648","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 : 2023-09-01DOI: 10.4208/jcm.2302-m2022-0246
Guangqiang Lan and Yu Jiang
{"title":"Convergence of Modified Truncated Euler-Maruyama Method for Stochastic Differential Equations with Hölder Diffusion Coefficients","authors":"Guangqiang Lan and Yu Jiang","doi":"10.4208/jcm.2302-m2022-0246","DOIUrl":"https://doi.org/10.4208/jcm.2302-m2022-0246","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"1 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135248623","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 : 2023-08-01DOI: 10.4208/jcm.2304-m2022-0243
Suna Ma, Hui-yuan Li, Zhimin Zhang, Hu Chen
{"title":"Efficient Spectral Methods for Eigenvalue Problems of the Integral Fractional Laplacian on a Ball of any Dimension","authors":"Suna Ma, Hui-yuan Li, Zhimin Zhang, Hu Chen","doi":"10.4208/jcm.2304-m2022-0243","DOIUrl":"https://doi.org/10.4208/jcm.2304-m2022-0243","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47863930","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 : 2023-06-01DOI: 10.4208/jcm.2210-m2021-0337
Dongyang Shi and Houchao Zhang null
{"title":"Convergence Analysis of Nonconforming Quadrilateral Finite Element Methods for Nonlinear Coupled Schrödinger-Helmholtz Equations","authors":"Dongyang Shi and Houchao Zhang null","doi":"10.4208/jcm.2210-m2021-0337","DOIUrl":"https://doi.org/10.4208/jcm.2210-m2021-0337","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135887813","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 : 2023-06-01DOI: 10.4208/jcm.2211-m2021-0293
Dingwen Li
Du Fort-Frankel finite difference method (FDM) was firstly proposed for linear diffu-sion equations with periodic boundary conditions by Du Fort and Frankel in 1953. It is an explicit and unconditionally von Neumann stable scheme. However, there has been no research work on numerical solutions of nonlinear Schr¨odinger equations with wave operator by using Du Fort-Frankel-type finite difference methods (FDMs). In this study, a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional (1D) and two-dimensional (2D) nonlinear Schr¨odinger equations with wave operator. By using the discrete energy method, it is shown that their solutions possess the discrete energy and mass conservative laws, and conditionally converge to exact solutions with an order of O ( τ 2 + h 2 x +( τ/h x ) 2 ) for 1D problem and an order of O ( τ 2 + h 2 x + h 2 y +( τ/h x ) 2 +( τ/h y ) 2 ) for 2D problem in H 1 -norm. Here, τ denotes time-step size, while, h x and h y represent spatial meshsizes in x - and y -directions, respectively. Then, by introducing a stabilized term, a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised. They not only preserve the discrete energies and masses, but also own much better stability than original schemes. Finally, numerical results demonstrate the theoretical analyses.
{"title":"Invariants-Preserving Du Fort-Frankel Schemes and Their Analyses for Nonlinear Schrödinger Equations With Wave Operator","authors":"Dingwen Li","doi":"10.4208/jcm.2211-m2021-0293","DOIUrl":"https://doi.org/10.4208/jcm.2211-m2021-0293","url":null,"abstract":"Du Fort-Frankel finite difference method (FDM) was firstly proposed for linear diffu-sion equations with periodic boundary conditions by Du Fort and Frankel in 1953. It is an explicit and unconditionally von Neumann stable scheme. However, there has been no research work on numerical solutions of nonlinear Schr¨odinger equations with wave operator by using Du Fort-Frankel-type finite difference methods (FDMs). In this study, a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional (1D) and two-dimensional (2D) nonlinear Schr¨odinger equations with wave operator. By using the discrete energy method, it is shown that their solutions possess the discrete energy and mass conservative laws, and conditionally converge to exact solutions with an order of O ( τ 2 + h 2 x +( τ/h x ) 2 ) for 1D problem and an order of O ( τ 2 + h 2 x + h 2 y +( τ/h x ) 2 +( τ/h y ) 2 ) for 2D problem in H 1 -norm. Here, τ denotes time-step size, while, h x and h y represent spatial meshsizes in x - and y -directions, respectively. Then, by introducing a stabilized term, a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised. They not only preserve the discrete energies and masses, but also own much better stability than original schemes. Finally, numerical results demonstrate the theoretical analyses.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44548979","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 : 2023-06-01DOI: 10.4208/nmtma.oa-2022-0202
Mingguang Geng and Shuli Sun
{"title":"Projection Improved SPAI Preconditioner for FGMRES","authors":"Mingguang Geng and Shuli Sun","doi":"10.4208/nmtma.oa-2022-0202","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0202","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195042","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 : 2023-06-01DOI: 10.4208/nmtma.oa-2022-0185
Xu Qian, Hong Zhang, Jingye Yan and Songhe Song
{"title":"Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation","authors":"Xu Qian, Hong Zhang, Jingye Yan and Songhe Song","doi":"10.4208/nmtma.oa-2022-0185","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0185","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135144382","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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