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Barycentric rational interpolation method of the Helmholtz equation with Irregular Domain 不规则区域Helmholtz方程的质心有理插值方法
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.16408
Miaomiao Yang, Wentao Ma, Y. Ge
{"title":"Barycentric rational interpolation method of the Helmholtz equation with Irregular Domain","authors":"Miaomiao Yang, Wentao Ma, Y. Ge","doi":"10.3846/mma.2023.16408","DOIUrl":"https://doi.org/10.3846/mma.2023.16408","url":null,"abstract":"In the work, a numerical method of the 2D Helmholtz equation with meshless interpolation collocation method is developed, which is defined in arbitrary domain with irregular shape. In our numerical method, based on the Chebyshev points, the partial derivatives and the spatial variables are discretized by the barycentric rational form basis function. After that the differential equations are simplified by employing differential matrix. To verify the the accuracy, effectiveness and stability in our method, some numerical tests based on the three types of different test points are adopted. Moreover, we can also verify that present method can be applied to both variable wave number problems and high wave number problems.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"270 1","pages":"330-351"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77899302","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}
引用次数: 0
On the Regularity criterion on One velocity Component for the micropolar fluid equations 微极流体方程单速度分量的正则性判据
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.15261
R. Agarwal, Ahmad M. Alghamdi, S. Gala, M. Ragusa
{"title":"On the Regularity criterion on One velocity Component for the micropolar fluid equations","authors":"R. Agarwal, Ahmad M. Alghamdi, S. Gala, M. Ragusa","doi":"10.3846/mma.2023.15261","DOIUrl":"https://doi.org/10.3846/mma.2023.15261","url":null,"abstract":"In this paper, we establish a regularity criterion for micropolar fluid flows in terms of the one component of the velocity in critical Morrey-Campanato space. More precisely, we show that if ...<∞, where 0<r<9/10 then the weak solution (u,w) is regular.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"1 1","pages":"271-284"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88799317","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}
引用次数: 4
On the inverse Problems for a family of integro-differential equations 一类积分-微分方程的反问题
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.16139
Kamran Suhaib, Asim Ilyas, S. Malik
{"title":"On the inverse Problems for a family of integro-differential equations","authors":"Kamran Suhaib, Asim Ilyas, S. Malik","doi":"10.3846/mma.2023.16139","DOIUrl":"https://doi.org/10.3846/mma.2023.16139","url":null,"abstract":"An integro-differential equation involving arbitrary kernel in time variable with a family of non-local boundary condition has been considered. Two inverse source problems for integro-differential equations are formulated and the unique-existence results for the solution of inverse source problems are presented. Some particular examples in support of our analysis are discussed.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"26 1","pages":"255-270"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83224679","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}
引用次数: 0
Asymptotic Analysis of Sturm-Liouville Problem with Dirichlet and nonlocal two-Point boundary conditions 具有Dirichlet和非局部两点边界条件的Sturm-Liouville问题的渐近分析
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.17617
A. Štikonas, E. Şen
{"title":"Asymptotic Analysis of Sturm-Liouville Problem with Dirichlet and nonlocal two-Point boundary conditions","authors":"A. Štikonas, E. Şen","doi":"10.3846/mma.2023.17617","DOIUrl":"https://doi.org/10.3846/mma.2023.17617","url":null,"abstract":"In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one–dimensional Sturm–Liouville equation with one classical Dirichlet type boundary condition and two-point nonlocal boundary condition. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic expansions of arbitrary order. We apply the obtained results to the problem with two-point nonlocal boundary condition.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"8 1","pages":"308-329"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86980854","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}
引用次数: 0
A collocation method for Fredholm integral equations of the First kind via iterative Regularization Scheme 基于迭代正则化方案的第一类Fredholm积分方程的配置方法
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.16453
T. Bechouat
{"title":"A collocation method for Fredholm integral equations of the First kind via iterative Regularization Scheme","authors":"T. Bechouat","doi":"10.3846/mma.2023.16453","DOIUrl":"https://doi.org/10.3846/mma.2023.16453","url":null,"abstract":"To solve the ill-posed integral equations, we use the regularized collocation method. This numerical method is a combination of the Legendre polynomials with non-stationary iterated Tikhonov regularization with fixed parameter. A theoretical justification of the proposed method under the required assumptions is detailed. Finally, numerical experiments demonstrate the efficiency of this method.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"13 1","pages":"237-254"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73946051","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}
引用次数: 0
On discrete-Time Models of Network Worm Propagation Generated by quadratic operators 二次算子生成的网络蠕虫传播的离散时间模型
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.15999
F. Adilova, U. Jamilov, A. Reinfelds
{"title":"On discrete-Time Models of Network Worm Propagation Generated by quadratic operators","authors":"F. Adilova, U. Jamilov, A. Reinfelds","doi":"10.3846/mma.2023.15999","DOIUrl":"https://doi.org/10.3846/mma.2023.15999","url":null,"abstract":"In this paper we consider the discrete-time dynamical systems generated by network worm propagation models based on the theory of quadratic stochastic operators(QSO). This approach simultaneously solves two important problems: exploring of the QSO trajectory‘s behavior, we described the set of limit points, thereby completely solved the main problem of dynamical systems (i), we showed a new application of the theory QSOs in worm propagation modelling (ii). We demonstrated that proposed discrete-time biologically-inspired model represents also realistic picture of the worm propagation process and such analytical models can be used in decision of some problems of computer networks.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"137 1","pages":"194-217"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89310445","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}
引用次数: 0
Collocation based Approximations for a class of fractional boundary Value Problems 一类分数边值问题的基于配置的近似
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.16359
Hanna Britt Soots, Kaido Lätt, A. Pedas
{"title":"Collocation based Approximations for a class of fractional boundary Value Problems","authors":"Hanna Britt Soots, Kaido Lätt, A. Pedas","doi":"10.3846/mma.2023.16359","DOIUrl":"https://doi.org/10.3846/mma.2023.16359","url":null,"abstract":"A boundary value problem for fractional integro-differential equations with weakly singular kernels is considered. The problem is reformulated as an integral equation of the second kind with respect to, the Caputo fractional derivative of y of order α, with 1 < α < 2, where y is the solution of the original problem. Using this reformulation, the regularity properties of both y and its Caputo derivative z are studied. Based on this information a piecewise polynomial collocation method is developed for finding an approximate solution zN of the reformulated problem. Using zN, an approximation yN for y is constructed and a detailed convergence analysis of the proposed method is given. In particular, the attainable order of convergence of the proposed method for appropriate values of grid and collocation parameters is established. To illustrate the performance of our approach, results of some numerical experiments are presented.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"77 1","pages":"218-236"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88544265","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}
引用次数: 1
Strong convergence to Common fixed Points using Ishikawa and Hybrid Methods for mean-Demiclosed mappings in Hilbert Spaces 希尔伯特空间中平均半闭映射的Ishikawa和混合方法的强收敛性
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.15843
Atsumasa Kondo
{"title":"Strong convergence to Common fixed Points using Ishikawa and Hybrid Methods for mean-Demiclosed mappings in Hilbert Spaces","authors":"Atsumasa Kondo","doi":"10.3846/mma.2023.15843","DOIUrl":"https://doi.org/10.3846/mma.2023.15843","url":null,"abstract":"In this paper, we establish a strong convergence theorem that approximates a common fixed point of two nonlinear mappings by comprehensively using an Ishikawa iterative method, a hybrid method, and a mean-valued iterative method. The shrinking projection method is also developed. The nonlinear mappings are a general type that includes nonexpansive mappings and other classes of well-known mappings. The two mappings are not assumed to be continuous or commutative. The main theorems in this paper generate a variety of strong convergence theorems including a type of “three-step iterative method”. An application to the variational inequality problem is also given.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"82 1","pages":"285-307"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86977692","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}
引用次数: 0
On the Functional Independence of the Riemann zeta-function 关于黎曼函数的泛函独立性
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-03-21 DOI: 10.3846/mma.2023.17157
V. Garbaliauskienė, R. Macaitienė, D. Šiaučiūnas
{"title":"On the Functional Independence of the Riemann zeta-function","authors":"V. Garbaliauskienė, R. Macaitienė, D. Šiaučiūnas","doi":"10.3846/mma.2023.17157","DOIUrl":"https://doi.org/10.3846/mma.2023.17157","url":null,"abstract":"In 1973, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i.e., that ζ(s) and its derivatives do not satisfy a certain equation with continuous functions. In the paper, we obtain a joint version of the Voronin theorem.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"57 1","pages":"352-359"},"PeriodicalIF":1.8,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74158737","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}
引用次数: 0
An Improved SimpleC Scheme for fluid Registration 改进的SimpleC流体配准方案
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2023-01-19 DOI: 10.3846/mma.2023.15482
M. Alahyane, A. Hakim, A. Laghrib, S. Raghay
{"title":"An Improved SimpleC Scheme for fluid Registration","authors":"M. Alahyane, A. Hakim, A. Laghrib, S. Raghay","doi":"10.3846/mma.2023.15482","DOIUrl":"https://doi.org/10.3846/mma.2023.15482","url":null,"abstract":"The image registration is always a strongly ill-posed problem, a stable numerical approach is then desired to better approximate the deformation vectors. This paper introduces an efficient numerical implementation of the Navier Stokes equation in the fluid image registration context. Although fluid registration approaches have succeeded in handling large image deformations, the numerical results are sometimes inconsistent and unexpected. This is related, in fact, to the used numerical scheme which does not take into consideration the different properties of the continuous operators. To take into account these properties, we use a robust numerical scheme based on finite volume with pressure correction. This scheme, which is called by the Semi-Implicit Method for Pressure-Linked Equation-Consistent (SIMPLEC), is known for its stability and consistency in fluid dynamics context. The experimental results demonstrate that the proposed method is more efficient and stable, visually and quantitatively, compared to some classical registration methods.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"17 1","pages":"71-90"},"PeriodicalIF":1.8,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83461980","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}
引用次数: 0
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