Pub Date : 2023-02-12DOI: 10.1007/s10543-023-00961-3
B. Jacobs, Fredrik Laurén, J. Nordström
{"title":"On the order reduction of approximations of fractional derivatives: an explanation and a cure","authors":"B. Jacobs, Fredrik Laurén, J. Nordström","doi":"10.1007/s10543-023-00961-3","DOIUrl":"https://doi.org/10.1007/s10543-023-00961-3","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-14"},"PeriodicalIF":1.5,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41482503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-12DOI: 10.1007/s10543-023-00949-z
D. Ivanenko, A. Kohatsu-Higa, A. Kulik
{"title":"Small time chaos approximations for heat kernels of multidimensional diffusions","authors":"D. Ivanenko, A. Kohatsu-Higa, A. Kulik","doi":"10.1007/s10543-023-00949-z","DOIUrl":"https://doi.org/10.1007/s10543-023-00949-z","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-34"},"PeriodicalIF":1.5,"publicationDate":"2023-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44920629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.1007/s10543-023-00950-6
Changqing Ye, Eric T. Chung
{"title":"Convergence of trigonometric and finite-difference discretization schemes for FFT-based computational micromechanics","authors":"Changqing Ye, Eric T. Chung","doi":"10.1007/s10543-023-00950-6","DOIUrl":"https://doi.org/10.1007/s10543-023-00950-6","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"25 1","pages":"1-26"},"PeriodicalIF":1.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81566853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-01DOI: 10.1007/s10543-023-00944-4
Zora Lj. Golubović, G. Milovanović
{"title":"Quadrature processes for efficient calculation of the Clausen functions","authors":"Zora Lj. Golubović, G. Milovanović","doi":"10.1007/s10543-023-00944-4","DOIUrl":"https://doi.org/10.1007/s10543-023-00944-4","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-20"},"PeriodicalIF":1.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46417221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-31DOI: 10.1007/s10543-023-00942-6
M. Hochbruck, M. Neher, Stefan Schrammer
{"title":"Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations","authors":"M. Hochbruck, M. Neher, Stefan Schrammer","doi":"10.1007/s10543-023-00942-6","DOIUrl":"https://doi.org/10.1007/s10543-023-00942-6","url":null,"abstract":"","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"63 1","pages":"1-24"},"PeriodicalIF":1.5,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49540924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with conditionally structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen–Cahn type. Important properties of such equations include maximum bound principle (MBP) and energy dissipation law; for the former, that means the absolute value of the solution is pointwisely bounded for all the time by some constant imposed by appropriate initial and boundary conditions. The model equation is first discretized in space by the central finite difference, then by iteratively using Duhamel’s formula, first- and second-order low regularity integrators (LRIs) are constructed for time discretization of the semi-discrete system. The proposed LRI schemes are proved to preserve the MBP and the energy stability in the discrete sense. Furthermore, their temporal error estimates are also successfully derived under a low regularity requirement that the exact solution of the semi-discrete problem is only assumed to be continuous in time. Numerical results show that the proposed LRI schemes are more accurate and have better convergence rates than classic exponential time differencing schemes, especially when the interfacial parameter approaches zero.
{"title":"Low regularity integrators for semilinear parabolic equations with maximum bound principles","authors":"Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Katharina Schratz","doi":"10.1007/s10543-023-00946-2","DOIUrl":"https://doi.org/10.1007/s10543-023-00946-2","url":null,"abstract":"This paper is concerned with conditionally structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen–Cahn type. Important properties of such equations include maximum bound principle (MBP) and energy dissipation law; for the former, that means the absolute value of the solution is pointwisely bounded for all the time by some constant imposed by appropriate initial and boundary conditions. The model equation is first discretized in space by the central finite difference, then by iteratively using Duhamel’s formula, first- and second-order low regularity integrators (LRIs) are constructed for time discretization of the semi-discrete system. The proposed LRI schemes are proved to preserve the MBP and the energy stability in the discrete sense. Furthermore, their temporal error estimates are also successfully derived under a low regularity requirement that the exact solution of the semi-discrete problem is only assumed to be continuous in time. Numerical results show that the proposed LRI schemes are more accurate and have better convergence rates than classic exponential time differencing schemes, especially when the interfacial parameter approaches zero.","PeriodicalId":55351,"journal":{"name":"BIT Numerical Mathematics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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