José Carmona, Antonio J. Martínez Aparicio, Pedro J. Martínez-Aparicio Martínez-Aparicio, Miguel Martínez-Teruel
We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is in Ω, u = 0 on ∂Ω, where Ω is a bounded open set of is a nonnegative function in L1(Ω) and g(x,s) is a Carathéodory function. In a framework where no solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.
我们分析了低阶项中的不同关系如何在奇异问题上导致相同的正则化效果，其模型在Ω， u = 0在∂Ω上，其中Ω是L1(Ω)中的有界开集，是一个非负函数，g(x,s)是一个carathsamodory函数。在不期望解的框架中，只要基准f与域边界或与低阶项方便地相互作用，我们就证明了它的存在性(正则化效应)。
{"title":"REGULARIZING EFFECT IN SINGULAR SEMILINEAR PROBLEMS","authors":"José Carmona, Antonio J. Martínez Aparicio, Pedro J. Martínez-Aparicio Martínez-Aparicio, Miguel Martínez-Teruel","doi":"10.3846/mma.2023.18616","DOIUrl":"https://doi.org/10.3846/mma.2023.18616","url":null,"abstract":"We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is in Ω, u = 0 on ∂Ω, where Ω is a bounded open set of is a nonnegative function in L1(Ω) and g(x,s) is a Carathéodory function. In a framework where no solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570149","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}
Nikolajus Kozulinas, Grigory Panasenko, Konstantinas Pileckas, Vytenis Šumskas
The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions in the vertices. Non-Newtonian rheology of the flow generates nonlinear equations on the graph. A new numerical method for second order nonlinear differential equations on the graph is introduced and numerically tested.
{"title":"NUMERICAL STUDY OF THE EQUATION ON THE GRAPH FOR THE STEADY STATE NON-NEWTONIAN FLOW IN THIN TUBE STRUCTURE","authors":"Nikolajus Kozulinas, Grigory Panasenko, Konstantinas Pileckas, Vytenis Šumskas","doi":"10.3846/mma.2023.18311","DOIUrl":"https://doi.org/10.3846/mma.2023.18311","url":null,"abstract":"The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions in the vertices. Non-Newtonian rheology of the flow generates nonlinear equations on the graph. A new numerical method for second order nonlinear differential equations on the graph is introduced and numerically tested.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569287","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}
Hammed A. Abass, Godwin C. Ugwunnadi, Lateef O. Jolaoso, Ojen K. Narain
In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.
在自反的Banach空间中，我们引入了一种计算分裂广义平衡问题和具有多个输出集的可数Bregman w -映射族不动点的公共解的Halpern迭代过程。我们证明了在一些温和条件下逼近上述问题解的一个强收敛结果。值得一提的是，本文采用的迭代算法在设计上不需要算子范数的先验知识。文中还给出了一些数值例子来说明所提出的迭代方法的性能。本文讨论的结果是对文献中许多相关结果的扩展和补充。
{"title":"ON SPLIT GENERALIZED EQUILIBRIUM AND FIXED POINT PROBLEMS OF BREGMAN W-MAPPINGS WITH MULTIPLE OUTPUT SETS IN REFLEXIVE BANACH SPACES","authors":"Hammed A. Abass, Godwin C. Ugwunnadi, Lateef O. Jolaoso, Ojen K. Narain","doi":"10.3846/mma.2023.17087","DOIUrl":"https://doi.org/10.3846/mma.2023.17087","url":null,"abstract":"In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570264","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}
Zhanar Imanova, Alexander Prokopenya, Mukhtar Minglibayev
A classical non-stationary three-body problem with two bodies of variable mass moving around the third body on quasi-periodic orbits is considered. In addition to the Newtonian gravitational attraction, the bodies are acted on by the reactive forces arising due to anisotropic variation of the masses. We show that Newtonian’s formalism may be generalized to the case of variable masses and equations of motion are derived in terms of the osculating elements of aperiodic motion on quasiconic sections. As equations of motion are not integrable the perturbative method is applied with the perturbing forces expanded into power series in terms of eccentricities and inclinations which are assumed to be small. Averaging these equations over the mean longitudes of the bodies in the absence of a mean-motion resonances, we obtain the differential equations describing the evolution of orbital parameters over long period of time. We solve the evolution equations numerically and demonstrate that the mass change modify essentially the system evolution.
{"title":"MODELLING THE EVOLUTION OF THE TWO-PLANETARY THREE-BODY SYSTEM OF VARIABLE MASSES","authors":"Zhanar Imanova, Alexander Prokopenya, Mukhtar Minglibayev","doi":"10.3846/mma.2023.18453","DOIUrl":"https://doi.org/10.3846/mma.2023.18453","url":null,"abstract":"A classical non-stationary three-body problem with two bodies of variable mass moving around the third body on quasi-periodic orbits is considered. In addition to the Newtonian gravitational attraction, the bodies are acted on by the reactive forces arising due to anisotropic variation of the masses. We show that Newtonian’s formalism may be generalized to the case of variable masses and equations of motion are derived in terms of the osculating elements of aperiodic motion on quasiconic sections. As equations of motion are not integrable the perturbative method is applied with the perturbing forces expanded into power series in terms of eccentricities and inclinations which are assumed to be small. Averaging these equations over the mean longitudes of the bodies in the absence of a mean-motion resonances, we obtain the differential equations describing the evolution of orbital parameters over long period of time. We solve the evolution equations numerically and demonstrate that the mass change modify essentially the system evolution.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569850","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}
Considering a minimization problem according to the Byrd-Nocedal measure function together with the secant equation, a diagonal quasi-Newton updating formula is suggested. To find the optimal elements of the updating matrix, the well-known algorithm of the alternating direction method of multipliers (ADMM) is employed. Moreover, convergence analysis is conducted based on a modified nonmonotone Armijo line search incorporating the simulated annealing strategy. Lastly, performance of the method is numerically tested on a set of CUTEr functions and on a smooth transcendental approximation of the compressive sensing problem. Across the computational spectrum, the given method turns out to be successful.
{"title":"A NONMONOTONE ADMM-BASED DIAGONAL QUASI-NEWTON UPDATE WITH APPLICATION TO THE COMPRESSIVE SENSING PROBLEM","authors":"Zohre Aminifard, Saman Babaie-Kafaki","doi":"10.3846/mma.2023.16993","DOIUrl":"https://doi.org/10.3846/mma.2023.16993","url":null,"abstract":"Considering a minimization problem according to the Byrd-Nocedal measure function together with the secant equation, a diagonal quasi-Newton updating formula is suggested. To find the optimal elements of the updating matrix, the well-known algorithm of the alternating direction method of multipliers (ADMM) is employed. Moreover, convergence analysis is conducted based on a modified nonmonotone Armijo line search incorporating the simulated annealing strategy. Lastly, performance of the method is numerically tested on a set of CUTEr functions and on a smooth transcendental approximation of the compressive sensing problem. Across the computational spectrum, the given method turns out to be successful.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570244","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}
In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).
{"title":"ALTERNATING DIRECTION IMPLICIT METHOD FOR POISSON EQUATION WITH INTEGRAL CONDITIONS","authors":"Olga Štikonienė, Mifodijus Sapagovas","doi":"10.3846/mma.2023.18029","DOIUrl":"https://doi.org/10.3846/mma.2023.18029","url":null,"abstract":"In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135618657","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}
A composite generalized Laguerre pseudospectral method for the nonlinear Fokker-Planck equations on the whole line is developed. Some composite generalized Laguerre interpolation approximation results are established. As an application, a composite Laguerre pseudospectral scheme is provided for the problems of the relaxation of fermion and boson gases. Convergence and stability of the scheme are proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.
{"title":"COMPOSITE LAGUERRE PSEUDOSPECTRAL METHOD FOR FOKKER-PLANCK EQUATIONS","authors":"Chuan Wang, Tianjun Wang, Youlin Shang","doi":"10.3846/mma.2023.17513","DOIUrl":"https://doi.org/10.3846/mma.2023.17513","url":null,"abstract":"A composite generalized Laguerre pseudospectral method for the nonlinear Fokker-Planck equations on the whole line is developed. Some composite generalized Laguerre interpolation approximation results are established. As an application, a composite Laguerre pseudospectral scheme is provided for the problems of the relaxation of fermion and boson gases. Convergence and stability of the scheme are proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135616550","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}
Kalyan Chakraborty, Shigeru Kanemitsu, Antanas Laurinčikas
In the paper, we prove that the set of discrete shifts of the Riemann zeta-function approximating analytic nonvanishing functions f1(s),...,fr(s) defined on has a positive density in the interval [N,N + M] with with real algebraic numbers a1,...,ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.
{"title":"ON JOINT DISCRETE UNIVERSALITY OF THE RIEMANN ZETA-FUNCTION IN SHORT INTERVALS","authors":"Kalyan Chakraborty, Shigeru Kanemitsu, Antanas Laurinčikas","doi":"10.3846/mma.2023.18884","DOIUrl":"https://doi.org/10.3846/mma.2023.18884","url":null,"abstract":"In the paper, we prove that the set of discrete shifts of the Riemann zeta-function approximating analytic nonvanishing functions f1(s),...,fr(s) defined on has a positive density in the interval [N,N + M] with with real algebraic numbers a1,...,ar linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617063","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}
A complete hypersingular integral equation of the second kind was obtained as a boundary integral equation for the diffraction and scattering problem of electromagnetic waves in space separated by the periodically placed non-perfectly conducting strips. The equation includes a singular integral that distinguishes it from the studied second-kind hypersingular equation. Our motivation is the need to have a numerical method for the equation, its applicability borders, and guaranteed convergence. The numerical method has the type of Nyström. The justification of the method envelops a proof of the theorem of existence and uniqueness of the solution and an estimate of the convergence rate of sequence of the approximate solutions to an exact solution.
{"title":"A NUMERICAL METHOD FOR SOLVING A COMPLETE HYPERSINGULAR INTEGRAL EQUATION OF THE SECOND KIND AND ITS JUSTIFICATION","authors":"Oleksii V. Kostenko","doi":"10.3846/mma.2023.14761","DOIUrl":"https://doi.org/10.3846/mma.2023.14761","url":null,"abstract":"A complete hypersingular integral equation of the second kind was obtained as a boundary integral equation for the diffraction and scattering problem of electromagnetic waves in space separated by the periodically placed non-perfectly conducting strips. The equation includes a singular integral that distinguishes it from the studied second-kind hypersingular equation. Our motivation is the need to have a numerical method for the equation, its applicability borders, and guaranteed convergence. The numerical method has the type of Nyström. The justification of the method envelops a proof of the theorem of existence and uniqueness of the solution and an estimate of the convergence rate of sequence of the approximate solutions to an exact solution.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135619815","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}
The amplitudes of the forced oscillations of a nano-structure conveying fluid are the solutions of an inhomogeneous integral-differential system. This is solved by an easily accessible scheme based on the variational iteration method (VIM), Galerkin’s method and the Laplace transform techniques. The presented method is accompanied by the study of the convergence of the iterative process and of the errors. In the literature, the dynamic response of a viscoelastic nanotube conveying fluid is frequently obtained by an iterative method. This leads to the double convolution products, whose presence will be avoided in the new method proposed in this paper. Thus, the numerical results will be obtained much faster and more accurately.
{"title":"Convergence of a variational iterative Algorithm for nonlocal vibrations Analysis of a nanotube Conveying fluid","authors":"Olga Martin","doi":"10.3846/mma.2023.16620","DOIUrl":"https://doi.org/10.3846/mma.2023.16620","url":null,"abstract":"The amplitudes of the forced oscillations of a nano-structure conveying fluid are the solutions of an inhomogeneous integral-differential system. This is solved by an easily accessible scheme based on the variational iteration method (VIM), Galerkin’s method and the Laplace transform techniques. The presented method is accompanied by the study of the convergence of the iterative process and of the errors. In the literature, the dynamic response of a viscoelastic nanotube conveying fluid is frequently obtained by an iterative method. This leads to the double convolution products, whose presence will be avoided in the new method proposed in this paper. Thus, the numerical results will be obtained much faster and more accurately.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69999395","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}
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