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An inexact Newton method with Inner preconditioned CG for non-uniformly Monotone Elliptic Problems 非均匀单调椭圆问题的内预条件非精确牛顿法
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-07-13 DOI: 10.3846/mma.2021.12899
B. Borsos
{"title":"An inexact Newton method with Inner preconditioned CG for non-uniformly Monotone Elliptic Problems","authors":"B. Borsos","doi":"10.3846/mma.2021.12899","DOIUrl":"https://doi.org/10.3846/mma.2021.12899","url":null,"abstract":"The present paper introduces an inexact Newton method, coupled with a preconditioned conjugate gradient method in inner iterations, for elliptic operators with non-uniformly monotone upper and lower bounds. Convergence is proved in Banach space level. The results cover real-life classes of elliptic problems. Numerical experiments reinforce the convergence results.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"53 1","pages":"383-394"},"PeriodicalIF":1.8,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77205692","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
Voronovskaya Type Results and operators Fixing two Functions Voronovskaya类型结果和操作符固定两个函数
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-07-13 DOI: 10.3846/mma.2021.13228
A. Acu, A. Mǎdutǎ, I. Raşa
{"title":"Voronovskaya Type Results and operators Fixing two Functions","authors":"A. Acu, A. Mǎdutǎ, I. Raşa","doi":"10.3846/mma.2021.13228","DOIUrl":"https://doi.org/10.3846/mma.2021.13228","url":null,"abstract":"The present paper deals with positive linear operators which fix two functions. The transfer of a given sequence (Ln) of positive linear operators to a new sequence (Kn) is investigated. A general procedure to construct sequences of positive linear operators fixing two functions which form an Extended Complete Chebyshev system is described. The Voronovskaya type formula corresponding to the new sequence which is strongly influenced by the nature of the fixed functions is obtained. In the last section our results are compared with other results existing in literature.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"2018 1","pages":"395-410"},"PeriodicalIF":1.8,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73324979","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: 8
Nonlinear Propagation of leaky TE-polarized electromagnetic waves in a Metamaterial Goubau Line 泄漏te极化电磁波在超材料沟包线中的非线性传播
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-07-13 DOI: 10.3846/MMA.2021.13077
E. Smolkin, Y. Smirnov
{"title":"Nonlinear Propagation of leaky TE-polarized electromagnetic waves in a Metamaterial Goubau Line","authors":"E. Smolkin, Y. Smirnov","doi":"10.3846/MMA.2021.13077","DOIUrl":"https://doi.org/10.3846/MMA.2021.13077","url":null,"abstract":"Propagation of leaky TE-polarized electromagnetic waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear metamaterial medium is studied. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"101 1","pages":"372-382"},"PeriodicalIF":1.8,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84728012","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
Identification of the Source for Full parabolic equations 全抛物型方程的源辨识
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-07-13 DOI: 10.3846/mma.2021.12700
G. F. Umbricht
{"title":"Identification of the Source for Full parabolic equations","authors":"G. F. Umbricht","doi":"10.3846/mma.2021.12700","DOIUrl":"https://doi.org/10.3846/mma.2021.12700","url":null,"abstract":"In this work, we consider the problem of identifying the time independent source for full parabolic equations in Rn from noisy data. This is an ill-posed problem in the sense of Hadamard. To compensate the factor that causes the instability, a family of parametric regularization operators is introduced, where the rule to select the value of the regularization parameter is included. This rule, known as regularization parameter choice rule, depends on the data noise level and the degree of smoothness that it is assumed for the source. The proof for the stability and convergence of the regularization criteria is presented and a Hölder type bound is obtained for the estimation error. Numerical examples are included to illustrate the effectiveness of this regularization approach.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"35 1","pages":"339-357"},"PeriodicalIF":1.8,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74842446","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: 2
Use of Galerkin Technique to the rolling of a plate in Deep water 利用伽辽金技术在深水中滚动钢板
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-27 DOI: 10.3846/mma.2021.12767
Swagata Ray, S. De, B. Mandal
{"title":"Use of Galerkin Technique to the rolling of a plate in Deep water","authors":"Swagata Ray, S. De, B. Mandal","doi":"10.3846/mma.2021.12767","DOIUrl":"https://doi.org/10.3846/mma.2021.12767","url":null,"abstract":"The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"77 1","pages":"209-222"},"PeriodicalIF":1.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89912060","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
Dynamics of a family of rational operators of Arbitrary degree 任意次有理数算子族的动力学
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI: 10.3846/mma.2021.12642
B. Campos, Jordi Canela, A. Garijo, P. Vindel
{"title":"Dynamics of a family of rational operators of Arbitrary degree","authors":"B. Campos, Jordi Canela, A. Garijo, P. Vindel","doi":"10.3846/mma.2021.12642","DOIUrl":"https://doi.org/10.3846/mma.2021.12642","url":null,"abstract":"In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and unboundedness of problematic parameters. After reparametrization, we observe that these rational maps belong to a more general family Oa,n,k of degree n+k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of Oa,n,k and discuss for which parameters n and k these operators would be suitable from the numerical point of view.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"6 1","pages":"188-208"},"PeriodicalIF":1.8,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89408051","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
Error Analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-Local boundary conditions 具有dirichlet型非局部边界条件的抛物方程的legende - galerkin谱法误差分析
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI: 10.3846/mma.2021.12865
Abdeldjalil Chattouh, K. Saoudi
{"title":"Error Analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-Local boundary conditions","authors":"Abdeldjalil Chattouh, K. Saoudi","doi":"10.3846/mma.2021.12865","DOIUrl":"https://doi.org/10.3846/mma.2021.12865","url":null,"abstract":"An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"11 1","pages":"287-303"},"PeriodicalIF":1.8,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79197103","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: 3
Development and Implementation of a Tenth-order Hybrid Block method for solving Fifth-order boundary Value Problems 求解五阶边值问题的十阶混合块法的发展与实现
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI: 10.3846/mma.2021.12940
H. Ramos, A. L. Momoh
{"title":"Development and Implementation of a Tenth-order Hybrid Block method for solving Fifth-order boundary Value Problems","authors":"H. Ramos, A. L. Momoh","doi":"10.3846/mma.2021.12940","DOIUrl":"https://doi.org/10.3846/mma.2021.12940","url":null,"abstract":"A hybrid convergent method of tenth-order is presented in this work for directly solving fifth-order boundary value problems in ordinary differential equations. A unique direct block approach is obtained by combining multiple Finite Difference Formulas which are derived via the collocation technique. The proposed method is fully analyzed and the existence and uniqueness of the discrete solution is established. Different numerical examples are considered and the results are compared with those provided by existing works in the literature. The comparison shows the good performance of the present method over some cited works in the literature, confirming the competitiveness and superiority of the new numerical integrator.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"139 1","pages":"267-286"},"PeriodicalIF":1.8,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86545208","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
Asymptotic Distribution of eigenvalues and eigenfunctions of a nonlocal boundary Value Problem 一类非局部边值问题的特征值和特征函数的渐近分布
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI: 10.3846/mma.2021.13056
E. Şen, A. Štikonas
{"title":"Asymptotic Distribution of eigenvalues and eigenfunctions of a nonlocal boundary Value Problem","authors":"E. Şen, A. Štikonas","doi":"10.3846/mma.2021.13056","DOIUrl":"https://doi.org/10.3846/mma.2021.13056","url":null,"abstract":"In this work, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the second order boundary-value problem with a Bitsadze–Samarskii type nonlocal boundary condition.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"54 1","pages":"253-266"},"PeriodicalIF":1.8,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73590780","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: 8
Correction to the Paper: An Energy Dissipative Spatial Discretization for the Regularized Compressible Navier-stokes-cahn-hilliard System of Equations (in Math. Model. Anal., 25(1): 110-129, https: //doi.org/10.3846/MMA.2020.10577) 论文更正:正则可压缩Navier-stokes-cahn-hilliard方程组的能量耗散空间离散化(数学)。模型。分析的， 25(1): 110-129, https: //doi.org/10.3846/MMA.2020.10577)
IF 1.8 3区 数学
Mathematical Modelling and Analysis Pub Date : 2021-05-26 DOI: 10.3846/mma.2021.14527
V. Balashov, A. Zlotnik
{"title":"Correction to the Paper: An Energy Dissipative Spatial Discretization for the Regularized Compressible Navier-stokes-cahn-hilliard System of Equations (in Math. Model. Anal., 25(1): 110-129, https: //doi.org/10.3846/MMA.2020.10577)","authors":"V. Balashov, A. Zlotnik","doi":"10.3846/mma.2021.14527","DOIUrl":"https://doi.org/10.3846/mma.2021.14527","url":null,"abstract":"We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"11 1","pages":"337-338"},"PeriodicalIF":1.8,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78656731","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
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