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Adaptation of the composite finite element framework for semilinear parabolic problems 针对半线性抛物线问题的复合有限元框架调整
Journal of Numerical Analysis and Approximation Theory Pub Date : 2024-04-16 DOI: 10.33993/jnaat531-1392
Anjaly Anand, T. Pramanick
{"title":"Adaptation of the composite finite element framework for semilinear parabolic problems","authors":"Anjaly Anand, T. Pramanick","doi":"10.33993/jnaat531-1392","DOIUrl":"https://doi.org/10.33993/jnaat531-1392","url":null,"abstract":"In this article, we discuss one of the subsections of finite element method (FEM), classified as the Composite Finite Element Method, abbreviated as CFE. Dimensionality reduction is the primary benefit of the CFE method as it helps to reduce the complexity for the domain space. The degrees of freedom is more in FEM, while compared to the CFE method. Here, the semilinear parabolic problem in a 2D convex polygonal domain is considered. The analysis of the semidiscrete method for the problem is carried out initially in the CFE framework. Here, the discretization would be carried out for the space co-ordinate. Then, fully discrete problem is taken into account, where both the spatial and time components get discretized. In the fully discrete case, the backward Euler method and the Crank-Nicolson method in the CFE framework is adapted for the semilinear problem. The properties of convergence are derived and the error estimates are examined. It is verified that the order of convergence is preserved. The results obtained from the numerical computations are also provided.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"26 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140696577","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}
引用次数: 0
A comparative study of Filon-type rules for oscillatory integrals 振荡积分的菲隆型规则比较研究
Journal of Numerical Analysis and Approximation Theory Pub Date : 2024-03-06 DOI: 10.33993/jnaat531-1380
H. Majidian
{"title":"A comparative study of Filon-type rules for oscillatory integrals","authors":"H. Majidian","doi":"10.33993/jnaat531-1380","DOIUrl":"https://doi.org/10.33993/jnaat531-1380","url":null,"abstract":"Our aim is to answer the following question: \"Among the Filon-type methods for computing oscillatory integrals, which one is the most efficient in practice?\". We first discuss why we should seek the answer among the family of Filon-Clenshaw-Curtis rules. A theoretical analysis accompanied by a set of numerical experiments reveals that the plain Filon-Clenshaw-Curtis rules reach a given accuracy faster than the (adaptive) extended Filon-Clenshaw-Curtis rules. The comparison is based on the CPU run-time for certain wave numbers (medium and large).","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"72 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140261268","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}
引用次数: 0
Local convergence analysis of frozen Steffensen-type methods under generalized conditions 广义条件下冻结斯蒂芬森型方法的局部收敛分析
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1160
I. Argyros, S. George
{"title":"Local convergence analysis of frozen Steffensen-type methods under generalized conditions","authors":"I. Argyros, S. George","doi":"10.33993/jnaat522-1160","DOIUrl":"https://doi.org/10.33993/jnaat522-1160","url":null,"abstract":"The goal in this study is to present a unified local convergence analysis of frozen Steffensen-type methods under generalized Lipschitz-type conditions for Banach space valued operators. We also use our new idea of restricted convergence domains, where we find a more precise location, where the iterates lie leading to at least as tight majorizing functions. Consequently, the new convergence criteria are weaker than in earlier works resulting to the expansion of the applicability of these methods. The conditions do not necessarily imply the differentiability of the operator involved. This way our method is suitable for solving equations and systems of equations.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"30 52","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139148215","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}
引用次数: 0
An extension of the Cheney-Sharma operator of the first kind 切尼-夏尔马第一类算子的扩展
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1373
Teodora Cătinaş, Iulia Buda
{"title":"An extension of the Cheney-Sharma operator of the first kind","authors":"Teodora Cătinaş, Iulia Buda","doi":"10.33993/jnaat522-1373","DOIUrl":"https://doi.org/10.33993/jnaat522-1373","url":null,"abstract":"We extend the Cheney-Sharma operators of the first kind using Stancu type technique and we study some approximation properties of the new operator. We calculate the moments, we study local approximation with respect to a K-functional and the preservation of the Lipschitz constant and order.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"2 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139151669","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}
引用次数: 0
Extension of primal-dual interior point method based on a kernel function for linear fractional problem 基于核函数的线性分数问题原始双内点法的扩展
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1349
Mousaab Bouafia, Adnan Yassine
{"title":"Extension of primal-dual interior point method based on a kernel function for linear fractional problem","authors":"Mousaab Bouafia, Adnan Yassine","doi":"10.33993/jnaat522-1349","DOIUrl":"https://doi.org/10.33993/jnaat522-1349","url":null,"abstract":"Our aim in this work is to extend the primal-dual interior point method based on a kernel function for linear fractional problem. We apply the techniques of kernel function-based interior point methods to solve a standard linear fractional program. By relying on the method of Charnes and Cooper [3], we transform the standard linear fractional problem into a linear program. This transformation will allow us to define the associated linear program and solve it efficiently using an appropriate kernel function. To show the efficiency of our approach, we apply our algorithm on the standard linear fractional programming found in numerical tests in the paper of A. Bennani et al. [4], we introduce the linear programming associated with this problem. We give three interior point conditions on this example, which depend on the dimension of the problem. We give the optimal solution for each linear program and each linear fractional program. We also obtain, using the new algorithm, the optimal solutions for the previous two problems. Moreover, some numerical results are illustrated to show the effectiveness of the method.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"6 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139148678","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}
引用次数: 0
Fuzzy Korovkin type Theorems via deferred Cesaro and deferred Euler equi-statistical convergence 通过延迟 Cesaro 和延迟 Euler 等式统计收敛的模糊 Korovkin 型定理
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1350
Purshottam Agrawal, Behar Baxhaku
{"title":"Fuzzy Korovkin type Theorems via deferred Cesaro and deferred Euler equi-statistical convergence","authors":"Purshottam Agrawal, Behar Baxhaku","doi":"10.33993/jnaat522-1350","DOIUrl":"https://doi.org/10.33993/jnaat522-1350","url":null,"abstract":"We establish a fuzzy Korovkin type approximation theorem by using (eq-stat^{D}_{CE})(deferred Ces'{a}ro and deferred Euler equi-statistical) convergence proposed by Saini et al. for continuous functions over ([a,b]). Further, we determine the rate of convergence via fuzzy modulus of continuity.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"305 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139152357","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}
引用次数: 0
The rate of convergence of bounded linear processes on spaces of continuous functions 连续函数空间上有界线性过程的收敛速率
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1326
H. Gonska
{"title":"The rate of convergence of bounded linear processes on spaces of continuous functions","authors":"H. Gonska","doi":"10.33993/jnaat522-1326","DOIUrl":"https://doi.org/10.33993/jnaat522-1326","url":null,"abstract":"Quantitative Korovkin-type theorems for approximation by bounded linear operators defined on (C(X,d)) are given, where ((X,d)) is a compact metric space. Special emphasis is on positive linear operators.As is known from previous work of Newman and Shapiro, Jimenez Pozo, Nishishiraho and the author, among others, there are two possible ways to obtain error estimates for bounded linear operator approximation: the so-called direct approach, and the smoothing technique.We give various generalizations and refinements of earlier results which were obtained by using both techniques. Furthermore, it will be shown that, in a certain sense, none of the two methods is superior to the other one.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"241 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139152771","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}
引用次数: 0
Localization of Nash-type equilibria for systems with partial variational structure 具有部分变分结构的系统的纳什型均衡局部化
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1356
Andrei Stan
{"title":"Localization of Nash-type equilibria for systems with partial variational structure","authors":"Andrei Stan","doi":"10.33993/jnaat522-1356","DOIUrl":"https://doi.org/10.33993/jnaat522-1356","url":null,"abstract":"In this paper, we aim to generalize an existing result by obtaining localized solutions within bounded convex sets, while also relaxing specific initial assumptions. To achieve this, we employ an iterative scheme that combines a fixed-point argument based on the Minty-Browder Theorem with a modified version of the Ekeland variational principle for bounded sets. An application to a system of second-order differential equations with Dirichlet boundary conditions is presented.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"64 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139151859","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}
引用次数: 0
Nonlinear random extrapolation estimates of (pi) under Dirichlet distributions 迪里希勒分布下的（pi）非线性随机外推法估计值
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1360
Shasha Wang, Zecheng Li, Wen-Qing Xu
{"title":"Nonlinear random extrapolation estimates of (pi) under Dirichlet distributions","authors":"Shasha Wang, Zecheng Li, Wen-Qing Xu","doi":"10.33993/jnaat522-1360","DOIUrl":"https://doi.org/10.33993/jnaat522-1360","url":null,"abstract":"We construct optimal nonlinear extrapolation estimates of (pi) based on random cyclic polygons generated from symmetric Dirichlet distributions. While the semiperimeter ( S_n ) and the area ( A_n ) of such random inscribed polygons and the semiperimeter (and area) ( S_n' ) of the corresponding random circumscribing polygons are known to converge to ( pi ) w.p.(1) and their distributions are also asymptotically normal as ( n to infty ), we study in this paper nonlinear extrapolations of the forms ( mathcal{W}_n = S_n^{alpha} A_n^{beta} S_n'^{, gamma} ) and ( mathcal{W}_n (p) = ( alpha S_n^p + beta A_n^p + gamma S_n'^{, p} )^{1/p} ) where ( alpha + beta + gamma = 1 ) and ( p neq 0 ). By deriving probabilistic asymptotic expansions with carefully controlled error estimates, we show that ( mathcal{W}_n ) and ( mathcal{W}_n (p) ) also converge to ( pi ) w.p.(1) and are asymptotically normal. Furthermore, to minimize the approximation error associated with ( mathcal{W}_n ) and ( mathcal{W}_n (p) ), the parameters must satisfy the optimality condition ( alpha + 4 beta - 2 gamma = 0 ). Our results generalize previous work on nonlinear extrapolations of ( pi ) which employ inscribed polygons only and the vertices are also assumed to be independently and uniformly distributed on the unit circle.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139148826","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}
引用次数: 0
New sufficient conditions for the solvability of a new class of Sylvester-like absolute value matrix equation 一类新的西尔维斯特类绝对值矩阵方程可解性的新充分条件
Journal of Numerical Analysis and Approximation Theory Pub Date : 2023-12-28 DOI: 10.33993/jnaat522-1321
Shubham Kumar, Deepmala, Roshan Lal Keshtwal
{"title":"New sufficient conditions for the solvability of a new class of Sylvester-like absolute value matrix equation","authors":"Shubham Kumar, Deepmala, Roshan Lal Keshtwal","doi":"10.33993/jnaat522-1321","DOIUrl":"https://doi.org/10.33993/jnaat522-1321","url":null,"abstract":"In this article, some new sufficient conditions for the unique solvability of a new class of Sylvester-like absolute value matrix equation (AXB - vert CXD vert =F) are given. This work is distinct from the published work by Li [Journal of Optimization Theory and Application, 195(2), 2022]. Some new conditions were also obtained, which were not covered by Li. We also provided an example in support of our result.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"11 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139152031","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}
引用次数: 0
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