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Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms 用拉普拉斯-傅立叶正弦联合变换求解四分之一平面非定常分数阶热传导
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1240
A. Aghili
{"title":"Solution to unsteady fractional heat conduction in the quarter-plane via the joint Laplace-Fourier sine transforms","authors":"A. Aghili","doi":"10.33993/jnaat501-1240","DOIUrl":"https://doi.org/10.33993/jnaat501-1240","url":null,"abstract":"In this article, the author implemented the joint transform method, for solving the boundary value problems of time fractional heat equation. The results reveal that the integral transform method is reliable and efficient. Illustrative examples are also provided.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128511213","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: 1
Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence 具有最优四阶收敛的potra - ptak型球收敛方法
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1247
I. Argyros, S. George
{"title":"Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence","authors":"I. Argyros, S. George","doi":"10.33993/jnaat501-1247","DOIUrl":"https://doi.org/10.33993/jnaat501-1247","url":null,"abstract":"We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used. \u0000In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129770271","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 two-point eighth-order method based on the weight function for solving nonlinear equations 基于权函数的两点八阶非线性方程求解方法
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1230
V. Torkashvand
{"title":"A two-point eighth-order method based on the weight function for solving nonlinear equations","authors":"V. Torkashvand","doi":"10.33993/jnaat501-1230","DOIUrl":"https://doi.org/10.33993/jnaat501-1230","url":null,"abstract":"In this work, we have designed a family of with-memory methods with eighth-order convergence. We have used the weight function technique. The proposed methods have three parameters. Three self-accelerating parameters are calculated in each iterative step employing only information from the current and all previous iteration. Numerical experiments are carried out to demonstrate the convergence and the e?ciency of our iterative method.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129143573","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
Nonuniform low-pass filters on non Archimedean local fields 非阿基米德局部场的非均匀低通滤波器
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-11-19 DOI: 10.33993/jnaat501-1241
O. Ahmad, A. Wani, Abid Ayub Hazari, N. Sheikh
{"title":"Nonuniform low-pass filters on non Archimedean local fields","authors":"O. Ahmad, A. Wani, Abid Ayub Hazari, N. Sheikh","doi":"10.33993/jnaat501-1241","DOIUrl":"https://doi.org/10.33993/jnaat501-1241","url":null,"abstract":"In real life application all signals are not obtained from uniform shifts; so there is a natural question regarding analysis and decompositions of this types of signals by a stable mathematical tool.\u0000Gabardo and Nashed (J. Funct. Anal. 158:209-241, 1998) filled this gap by the concept of nonuniform multiresolution analysis. In this setting, the associated translation set (Lambda =left{ 0,r/Nright}+2,mathbb Z) is no longer a discrete subgroup of (mathbb R) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair.\u0000The main aim of this article is to provide the characterization of nonuniform low-pass filters on non-Archimedean local fields.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129130684","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
Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render 关于Aldaz, Kounchev和Render的bernstein型算子的注释
Journal of Numerical Analysis and Approximation Theory Pub Date : 2021-08-17 DOI: 10.33993/jnaat501-1237
A. Acu, H. Gonska, M. Heilmann
{"title":"Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render","authors":"A. Acu, H. Gonska, M. Heilmann","doi":"10.33993/jnaat501-1237","DOIUrl":"https://doi.org/10.33993/jnaat501-1237","url":null,"abstract":"The Bernstein-type operator of Aldaz, Kounchev and Render (2009) is discussed. New direct results in terms of the classical second order modulus as well as in a modification following Marsden and Schoenberg are given.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130046470","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: 3
Optimal properties for deficient quartic splines of Marsden type 马斯登型缺四次样条的最优性质
Journal of Numerical Analysis and Approximation Theory Pub Date : 2020-12-31 DOI: 10.33993/jnaat492-1228
A. Bica, Diana Curilă-Popescu, M. Curila
{"title":"Optimal properties for deficient quartic splines of Marsden type","authors":"A. Bica, Diana Curilă-Popescu, M. Curila","doi":"10.33993/jnaat492-1228","DOIUrl":"https://doi.org/10.33993/jnaat492-1228","url":null,"abstract":"In this work, we obtain an improved error estimate in the interpolation with the Hermite (C^{2})-smooth deficient complete quartic spline that has the distribution of nodes following the Marsden type scheme and investigate the possibilities to compute the derivatives on the knots such that the obtained spline (Sin C^{1}[a,b]) has minimal curvature and minimal (L^{2})-norm of (S^{prime }) and (S^{prime prime prime }). In each case, the interpolation error estimate is performed in terms of the modulus of continuity.%MCEPASTEBIN%","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128788014","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: 2
Generalized Ostrowski inequalities and computational integration 广义Ostrowski不等式与计算积分
Journal of Numerical Analysis and Approximation Theory Pub Date : 2020-12-31 DOI: 10.33993/jnaat492-1224
Nazia Irshad, Asif R Khan, Hina Musharraf
{"title":"Generalized Ostrowski inequalities and computational integration","authors":"Nazia Irshad, Asif R Khan, Hina Musharraf","doi":"10.33993/jnaat492-1224","DOIUrl":"https://doi.org/10.33993/jnaat492-1224","url":null,"abstract":"We state and prove three generalized results related to Ostrowski inequality by using differentiable functions which are bounded, bounded below only and bounded above only, respectively. From our proposed results we get number of established results as our special cases.\u0000Some applications in numerical integration are also given which gives us some standard and nonstandard quadrature rules.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128860866","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
Extended convergence analysis of Newton-Potra solver for equations 方程Newton-Potra解算器的扩展收敛性分析
Journal of Numerical Analysis and Approximation Theory Pub Date : 2020-12-31 DOI: 10.33993/jnaat492-1186
I. Argyros, S. Shakhno, Yurii Shunkin, H. Yarmola
{"title":"Extended convergence analysis of Newton-Potra solver for equations","authors":"I. Argyros, S. Shakhno, Yurii Shunkin, H. Yarmola","doi":"10.33993/jnaat492-1186","DOIUrl":"https://doi.org/10.33993/jnaat492-1186","url":null,"abstract":"In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839.... The radius of the convergence ball and convergence order of the investigated solver are determined in an earlier paper. Modifications of previous conditions leads to extended convergence domain. These advantages are obtained under the same computational effort.\u0000Numerical experiments are carried out on the test examples with nondifferentiable operator.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131097301","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
Approximation on the regular hexagon 正六边形的近似
Journal of Numerical Analysis and Approximation Theory Pub Date : 2020-12-31 DOI: 10.33993/jnaat492-1229
A. Guven
{"title":"Approximation on the regular hexagon","authors":"A. Guven","doi":"10.33993/jnaat492-1229","DOIUrl":"https://doi.org/10.33993/jnaat492-1229","url":null,"abstract":"\u0000\u0000\u0000The degree of trigonometric approximation of continuous functions, which are periodic with respect to the hexagon lattice, is estimated in uniform and Hölder norms.\u0000Approximating trigonometric polynomials are matrix means of hexagonal Fourier series.\u0000\u0000\u0000","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129421304","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
Basin attractors for derivative-free methods to find simple roots of nonlinear equations 盆吸引子无导数求非线性方程单根的方法
Journal of Numerical Analysis and Approximation Theory Pub Date : 2020-12-31 DOI: 10.33993/jnaat492-1232
B. Neta
{"title":"Basin attractors for derivative-free methods to find simple roots of nonlinear equations","authors":"B. Neta","doi":"10.33993/jnaat492-1232","DOIUrl":"https://doi.org/10.33993/jnaat492-1232","url":null,"abstract":" Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference. Clearly such method will need an additional starting value. Here we consider several derivative-free methods and compare them using the idea of basin of attraction.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125617126","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: 3
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