Pub Date : 2022-06-01DOI: 10.4208/nmtma.oa-2022-0010s
Changpin Li null, Zhen Wang
{"title":"L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation","authors":"Changpin Li null, Zhen Wang","doi":"10.4208/nmtma.oa-2022-0010s","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0010s","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42173614","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 : 2022-06-01DOI: 10.4208/nmtma.oa-2021-0181
Ting Li, Changying Liu, Bin Wang
In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment. AMS subject classifications: 65P10, 65L05
{"title":"Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems","authors":"Ting Li, Changying Liu, Bin Wang","doi":"10.4208/nmtma.oa-2021-0181","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0181","url":null,"abstract":"In this paper, we investigate the long-time near-conservations of energy and kinetic energy by the widely used exponential integrators to highly oscillatory conservative systems. The modulated Fourier expansions of two kinds of exponential integrators have been constructed and the long-time numerical conservations of energy and kinetic energy are obtained by deriving two almost-invariants of the expansions. Practical examples of the methods are given and the theoretical results are confirmed and demonstrated by a numerical experiment. AMS subject classifications: 65P10, 65L05","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47656370","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 : 2022-06-01DOI: 10.4208/nmtma.oa-2021-0164
Hassan Bozorgmanesh, Masoud Hajarian null, Anthony T. Chronopoulos
. It is known that every tensor has an associated semi-symmetric tensor. The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form. In particular, a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems. In addition, every tensor has the same eigenvalues as its corresponding semi-symmetric form, also a corresponding semi-symmetric tensor inherits properties like being circulant, Toeplitz, Z -tensor, M -tensor, H -tensor and some oth-ers. Also, there are a two-way connection for properties like being positive definite, P -tensor, semi-positive, primitive and several others.
{"title":"The Relation Between a Tensor and Its Associated Semi-Symmetric Form","authors":"Hassan Bozorgmanesh, Masoud Hajarian null, Anthony T. Chronopoulos","doi":"10.4208/nmtma.oa-2021-0164","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0164","url":null,"abstract":". It is known that every tensor has an associated semi-symmetric tensor. The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form. In particular, a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems. In addition, every tensor has the same eigenvalues as its corresponding semi-symmetric form, also a corresponding semi-symmetric tensor inherits properties like being circulant, Toeplitz, Z -tensor, M -tensor, H -tensor and some oth-ers. Also, there are a two-way connection for properties like being positive definite, P -tensor, semi-positive, primitive and several others.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44256939","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 : 2022-06-01DOI: 10.4208/nmtma.oa-2021-0038
Rui Li, Jun-Feng Yin null, Zhi-lin Li
We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems. Applying the preconditioning technique we also construct the preconditioned version of the proposed method. Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric. Meanwhile, when the real part and the imaginary part of the coefficient matrix are symmetric positive definite, we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge. Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods. AMS subject classifications: 65F10, 65F15, 65T10
{"title":"A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems","authors":"Rui Li, Jun-Feng Yin null, Zhi-lin Li","doi":"10.4208/nmtma.oa-2021-0038","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0038","url":null,"abstract":"We propose a variant modified skew-normal splitting iterative method to solve a class of large sparse non-Hermitian positive definite linear systems. Applying the preconditioning technique we also construct the preconditioned version of the proposed method. Theoretical analysis shows that the proposed method is unconditionally convergent even when the real part and the imaginary part of the coefficient matrix are non-symmetric. Meanwhile, when the real part and the imaginary part of the coefficient matrix are symmetric positive definite, we prove that the preconditioned variant modified skew-normal splitting iterative method will also unconditionally converge. Numerical experiments are presented to illustrate the efficiency of the proposed method and show better performance of it when compared with some other methods. AMS subject classifications: 65F10, 65F15, 65T10","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49515946","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 : 2022-01-01DOI: 10.1007/978-3-031-32412-3_7
F. Benkhaldoun, A. Bradji
{"title":"SUSHI for a Non-linear Time Fractional Diffusion Equation with a Time Independent Delay","authors":"F. Benkhaldoun, A. Bradji","doi":"10.1007/978-3-031-32412-3_7","DOIUrl":"https://doi.org/10.1007/978-3-031-32412-3_7","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"42 1","pages":"73-84"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78539462","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 : 2022-01-01DOI: 10.1007/978-3-031-32412-3_20
L. Milev, N. Naidenov
{"title":"An Inequality for Polynomials on the Standard Simplex","authors":"L. Milev, N. Naidenov","doi":"10.1007/978-3-031-32412-3_20","DOIUrl":"https://doi.org/10.1007/978-3-031-32412-3_20","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"12 1","pages":"221-232"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85755406","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 : 2022-01-01DOI: 10.1007/978-3-031-32412-3_4
Atanas Z. Atanasov, M. Koleva, L. Vulkov
{"title":"Parameter Estimation Inspired by Temperature Measurements for a Chemotactic Model of Honeybee Thermoregulation","authors":"Atanas Z. Atanasov, M. Koleva, L. Vulkov","doi":"10.1007/978-3-031-32412-3_4","DOIUrl":"https://doi.org/10.1007/978-3-031-32412-3_4","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"11 1","pages":"36-47"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87642963","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 : 2022-01-01DOI: 10.1007/978-3-031-32412-3_8
M. Borisov, S. Markov
{"title":"On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving Uncertainties","authors":"M. Borisov, S. Markov","doi":"10.1007/978-3-031-32412-3_8","DOIUrl":"https://doi.org/10.1007/978-3-031-32412-3_8","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"71 1","pages":"85-99"},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79577073","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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