Pub Date : 2024-06-20DOI: 10.1007/s13226-024-00615-2
Jun Li, Lingsheng Meng, Shu-Xin Miao
In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized relaxed BPS (GRBPS) preconditioner is proposed for generalized saddle point linear system. Spectral properties of the GRBPS preconditioned matrix are analyzed in details. Theoretical results show that the eigenvalues of the preconditioned matrix are clustered at only two points when the iteration parameters are close to zero. Finally, a numerical example is provided to verify the efficiency of the GRBPS preconditioner.
{"title":"A generalized relaxed block positive-semidefinite splitting preconditioner for generalized saddle point linear system","authors":"Jun Li, Lingsheng Meng, Shu-Xin Miao","doi":"10.1007/s13226-024-00615-2","DOIUrl":"https://doi.org/10.1007/s13226-024-00615-2","url":null,"abstract":"<p>In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized relaxed BPS (GRBPS) preconditioner is proposed for generalized saddle point linear system. Spectral properties of the GRBPS preconditioned matrix are analyzed in details. Theoretical results show that the eigenvalues of the preconditioned matrix are clustered at only two points when the iteration parameters are close to zero. Finally, a numerical example is provided to verify the efficiency of the GRBPS preconditioner.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-19DOI: 10.1007/s13226-024-00614-3
Reena Koundal
In this work, novel type of fractional polynomials are proposed as the generalization to shifted Lucas polynomials, which are called as fractional shifted Lucas polynomials. Useful operational matrices are developed here utilizing the newly established analytical formula for the construction of the numerical scheme. Further, a theorem for the calculation of Caputo fractional derivative is proved and an useful remark is provided for integer order derivative. At the core of the work, the task is to use collocation points for tackling the multi-term differential equations/multi-order differential equations (MODEs/MTDEs). To develop the strong background for the proposed scheme, error analysis is performed. The algorithm of the scheme is examined through some test examples of MODEs/MTDEs, and comparisons are made with other existing methods.
{"title":"Treatment of fractional multi-order/multi-term differential equations: utilizing fractional shifted Lucas polynomials","authors":"Reena Koundal","doi":"10.1007/s13226-024-00614-3","DOIUrl":"https://doi.org/10.1007/s13226-024-00614-3","url":null,"abstract":"<p>In this work, novel type of fractional polynomials are proposed as the generalization to shifted Lucas polynomials, which are called as fractional shifted Lucas polynomials. Useful operational matrices are developed here utilizing the newly established analytical formula for the construction of the numerical scheme. Further, a theorem for the calculation of Caputo fractional derivative is proved and an useful remark is provided for integer order derivative. At the core of the work, the task is to use collocation points for tackling the multi-term differential equations/multi-order differential equations (MODEs/MTDEs). To develop the strong background for the proposed scheme, error analysis is performed. The algorithm of the scheme is examined through some test examples of MODEs/MTDEs, and comparisons are made with other existing methods.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By applying the lopsided technology to the preconditioned modified quasi-Hermitian and skew-Hermitian splitting (PMQHSS) iteration method, we construct a lopsided PMQHSS (LPMQHSS) iteration method for solving complex symmetric linear equations. We discuss the convergence properties of the LPMQHSS method. Specially, the convergence properties of the LPMQHSS method with (V=T) are established. In addition, we also give another new iteration method, referred to as double lopsided PMQHSS (DLPMQHSS) iteration method. The convergence conditions of the DLPMQHSS iteration method are analyzed. The proposed LPMQHSS and DLPMQHSS methods have faster convergence rates than the PMQHSS one. Numerical experiments are reported to illustrate the feasibility and effectiveness of the proposed methods.
{"title":"Lopsided PMQHSS and double lopsided PMQHSS iteration methods for solving complex symmetric linear equations","authors":"Bei-Bei Li, Jing-Jing Cui, Zheng-Ge Huang, Xiao-Feng Xie","doi":"10.1007/s13226-024-00618-z","DOIUrl":"https://doi.org/10.1007/s13226-024-00618-z","url":null,"abstract":"<p>By applying the lopsided technology to the preconditioned modified quasi-Hermitian and skew-Hermitian splitting (PMQHSS) iteration method, we construct a lopsided PMQHSS (LPMQHSS) iteration method for solving complex symmetric linear equations. We discuss the convergence properties of the LPMQHSS method. Specially, the convergence properties of the LPMQHSS method with <span>(V=T)</span> are established. In addition, we also give another new iteration method, referred to as double lopsided PMQHSS (DLPMQHSS) iteration method. The convergence conditions of the DLPMQHSS iteration method are analyzed. The proposed LPMQHSS and DLPMQHSS methods have faster convergence rates than the PMQHSS one. Numerical experiments are reported to illustrate the feasibility and effectiveness of the proposed methods.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-19DOI: 10.1007/s13226-024-00623-2
S. Veeramani, Jadav Ganesh
In this note, we study the stability of the approximate pseudospectrum correspondences by investigating its continuity nature.
在本说明中，我们通过研究近似伪谱对应关系的连续性来研究其稳定性。
{"title":"Some remarks on the stability of approximate pseudospectrum","authors":"S. Veeramani, Jadav Ganesh","doi":"10.1007/s13226-024-00623-2","DOIUrl":"https://doi.org/10.1007/s13226-024-00623-2","url":null,"abstract":"<p>In this note, we study the stability of the approximate pseudospectrum correspondences by investigating its continuity nature.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1007/s13226-024-00611-6
M. Younus Bhat
Bhat in Annal. Univ. Craiova, Math. Comp. Scien. Series 49: 2(2022), 401-410 has studied nonhomogeneous wavelet bi-frames in Sobolev spaces on local fields of positive characteristic. In this paper, we used the same platform to characterize nonhomogeneous wavelet bi-frames for the reducing subspaces of Sobolev spaces over local fields of positive characteristics.
Bhat in Annal.Univ. Craiova, Math.Comp.Scien.Series 49: 2(2022), 401-410 中研究了正特征局部域上索波列夫空间中的非均质小波双帧。在本文中，我们使用相同的平台来表征正特征局部域上索波列夫空间的还原子空间的非均质小波双框架。
{"title":"Nonhomogeneous Wavelet Bi-frames for Reducing Subspaces of $$H^s(K)$$ and their Characterization","authors":"M. Younus Bhat","doi":"10.1007/s13226-024-00611-6","DOIUrl":"https://doi.org/10.1007/s13226-024-00611-6","url":null,"abstract":"<p>Bhat in <i>Annal. Univ. Craiova, Math. Comp. Scien. Series </i> 49: 2(2022), 401-410 has studied nonhomogeneous wavelet bi-frames in Sobolev spaces on local fields of positive characteristic. In this paper, we used the same platform to characterize nonhomogeneous wavelet bi-frames for the reducing subspaces of Sobolev spaces over local fields of positive characteristics.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"141 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-13DOI: 10.1007/s13226-024-00587-3
K. Ansari, Faruk Özger
{"title":"Pointwise and weighted estimates for Bernstein-Kantorovich type operators including beta function","authors":"K. Ansari, Faruk Özger","doi":"10.1007/s13226-024-00587-3","DOIUrl":"https://doi.org/10.1007/s13226-024-00587-3","url":null,"abstract":"","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"58 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-12DOI: 10.1007/s13226-024-00600-9
Zhiqiang Shao
{"title":"The Riemann problem with delta initial data with Dirac delta function in both components for a pressureless gas dynamic model","authors":"Zhiqiang Shao","doi":"10.1007/s13226-024-00600-9","DOIUrl":"https://doi.org/10.1007/s13226-024-00600-9","url":null,"abstract":"","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"129 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141351589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-10DOI: 10.1007/s13226-024-00613-4
J. Kumar, S. Singh, S. Arora, J. Dabas
In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equation with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration by imposing the theory of (C_0)-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example demonstrates the feasibility of derived abstract results.
{"title":"Total controllability of nonlocal semilinear functional evolution equations with non-instantaneous impulses","authors":"J. Kumar, S. Singh, S. Arora, J. Dabas","doi":"10.1007/s13226-024-00613-4","DOIUrl":"https://doi.org/10.1007/s13226-024-00613-4","url":null,"abstract":"<p>In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equation with non-instantaneous impulses and finite delay in Hilbert spaces. A set of sufficient conditions of total controllability is obtained for the evolution system under consideration by imposing the theory of <span>(C_0)</span>-semigroup and Banach fixed point theorem. We also established the total controllability results for a functional integro-differential equation. Finally, an example demonstrates the feasibility of derived abstract results.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"13 50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-10DOI: 10.1007/s13226-024-00617-0
C. Anabanti, A. K. Asboei
{"title":"Harmonic mean Sylow numbers of nonsolvable groups","authors":"C. Anabanti, A. K. Asboei","doi":"10.1007/s13226-024-00617-0","DOIUrl":"https://doi.org/10.1007/s13226-024-00617-0","url":null,"abstract":"","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"112 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141361059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-07DOI: 10.1007/s13226-024-00608-1
Manoj Kumar, Aman Jhinga, Varsha Daftardar-Gejji
{"title":"Erratum to: Higher order numerical methods for fractional delay differential equations","authors":"Manoj Kumar, Aman Jhinga, Varsha Daftardar-Gejji","doi":"10.1007/s13226-024-00608-1","DOIUrl":"https://doi.org/10.1007/s13226-024-00608-1","url":null,"abstract":"","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":" 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141374140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号