Pub Date : 2024-09-01DOI: 10.1134/s0965542524700738
Çağla Çelemoğlu
Abstract
Here, we first introduce complex Narayana numbers. Then, we describe a new quaternion sequence whose coefficients consist of complex Narayana numbers and that we named with complex Narayana quaternions. We also give the generating function, exponential generating function, Binet formula, and summation formulas for these sequences. Finally, we obtain a matrix representation of complex Narayana quaternions and make an application related to the matrix representation of complex Narayana quaternions.
{"title":"Complex Narayana Quaternions","authors":"Çağla Çelemoğlu","doi":"10.1134/s0965542524700738","DOIUrl":"https://doi.org/10.1134/s0965542524700738","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Here, we first introduce complex Narayana numbers. Then, we describe a new quaternion sequence whose coefficients consist of complex Narayana numbers and that we named with complex Narayana quaternions. We also give the generating function, exponential generating function, Binet formula, and summation formulas for these sequences. Finally, we obtain a matrix representation of complex Narayana quaternions and make an application related to the matrix representation of complex Narayana quaternions.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700659
F. V. Lubyshev, M. E. Fairuzov
Abstract
We study difference approximations of an optimal control problem with a boundary observation of the conormal derivative of the state described by the Dirichlet problem for semilinear elliptic equations with controls involved in coefficients of the convective transport operator and in the nonlinear term of the equation. The well-posedness of the optimal control problem is examined. Difference approximations for the optimal control problem are constructed. The convergence of the approximations with respect to the functional and control is analyzed. A regularization of the approximations is constructed.
{"title":"Approximation of Optimal Control Problems for Semilinear Elliptic Convection–Diffusion Equations with Boundary Observation of the Conormal Derivative and with Controls in Coefficients of the Convective Transport Operator and in Nonlinear Term of the Equation","authors":"F. V. Lubyshev, M. E. Fairuzov","doi":"10.1134/s0965542524700659","DOIUrl":"https://doi.org/10.1134/s0965542524700659","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study difference approximations of an optimal control problem with a boundary observation of the conormal derivative of the state described by the Dirichlet problem for semilinear elliptic equations with controls involved in coefficients of the convective transport operator and in the nonlinear term of the equation. The well-posedness of the optimal control problem is examined. Difference approximations for the optimal control problem are constructed. The convergence of the approximations with respect to the functional and control is analyzed. A regularization of the approximations is constructed.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700611
Yu. A. Eremin, V. V. Lopushenko
Abstract
The discrete sources method is used to develop a mathematical model for comparative analysis of the influence exerted on the optical properties of alkaline and noble metal nanoparticles placed in a dense outer medium when the bulk and surface quantum effects are taken into account. A substantial difference between the manifestations of the bulk and surface quantum effects in alkaline particles is demonstrated. Specifically, in the case of the bulk quantum effect, the surface plasmon resonance in alkaline particles exhibits a shift toward shorter wavelengths (blue shift), while the surface effect leads to a shift toward longer wavelengths (red shift). It is shown that this shift depends substantially on the outer medium density and can reach 50 nm in the spectral range.
{"title":"Comparative Analysis of the Influence of Surface Quantum Effects on Optical Characteristics of Alkali and Noble Metallic Nanoparticles","authors":"Yu. A. Eremin, V. V. Lopushenko","doi":"10.1134/s0965542524700611","DOIUrl":"https://doi.org/10.1134/s0965542524700611","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The discrete sources method is used to develop a mathematical model for comparative analysis of the influence exerted on the optical properties of alkaline and noble metal nanoparticles placed in a dense outer medium when the bulk and surface quantum effects are taken into account. A substantial difference between the manifestations of the bulk and surface quantum effects in alkaline particles is demonstrated. Specifically, in the case of the bulk quantum effect, the surface plasmon resonance in alkaline particles exhibits a shift toward shorter wavelengths (blue shift), while the surface effect leads to a shift toward longer wavelengths (red shift). It is shown that this shift depends substantially on the outer medium density and can reach 50 nm in the spectral range.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700714
E. V. Chizhonkov
Abstract
An implicit MacCormack-type scheme is constructed for a kinetic plasma model based on the Vlasov–Ampère equations. As compared with the explicit scheme, it has a weaker stability restriction, but preserves computational efficiency, i.e., it does not involve inner iterations. The error of the total energy corresponds to a second-order accurate algorithm, and the total charge (number of particles) is preserved at the grid level. The formation of plasma waves excited by a short intense laser pulse is modeled as an example.
{"title":"Numerical Solution of the Vlasov–Ampère Equations","authors":"E. V. Chizhonkov","doi":"10.1134/s0965542524700714","DOIUrl":"https://doi.org/10.1134/s0965542524700714","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An implicit MacCormack-type scheme is constructed for a kinetic plasma model based on the Vlasov–Ampère equations. As compared with the explicit scheme, it has a weaker stability restriction, but preserves computational efficiency, i.e., it does not involve inner iterations. The error of the total energy corresponds to a second-order accurate algorithm, and the total charge (number of particles) is preserved at the grid level. The formation of plasma waves excited by a short intense laser pulse is modeled as an example.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700593
P. N. Vabishchevich
Abstract
Difference methods are widely used for the approximate solution of boundary value problems for partial differential equations. Grid approximations are most simply constructed when the computational domain is divided into rectangular cells. Typically, the grid nodes coincide with the vertices of the cells. In addition to such node-center approximations, grids with nodes at the centers of cells are also used. It is convenient to formulate boundary value problems in terms of invariant operators of vector (tensor) analysis, which are associated with corresponding grid analogs. In this work, analogs of the gradient and divergence operators are constructed on non-standard rectangular grids the nodes of which consist of both the vertices of the computational cells and their centers. The proposed approach is illustrated using approximations of a boundary value problem for a stationary two-dimensional convection–diffusion equation. The key features of constructing approximations for vector problems are discussed with a focus on applied problems of the mechanics of solids.
{"title":"Difference Operator Approximations on Nonstandard Rectangular Grid","authors":"P. N. Vabishchevich","doi":"10.1134/s0965542524700593","DOIUrl":"https://doi.org/10.1134/s0965542524700593","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Difference methods are widely used for the approximate solution of boundary value problems for partial differential equations. Grid approximations are most simply constructed when the computational domain is divided into rectangular cells. Typically, the grid nodes coincide with the vertices of the cells. In addition to such node-center approximations, grids with nodes at the centers of cells are also used. It is convenient to formulate boundary value problems in terms of invariant operators of vector (tensor) analysis, which are associated with corresponding grid analogs. In this work, analogs of the gradient and divergence operators are constructed on non-standard rectangular grids the nodes of which consist of both the vertices of the computational cells and their centers. The proposed approach is illustrated using approximations of a boundary value problem for a stationary two-dimensional convection–diffusion equation. The key features of constructing approximations for vector problems are discussed with a focus on applied problems of the mechanics of solids.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700726
A. A. Shevyrin, Ye. A. Bondar
Abstract
Procedures of the Direct Simulation Monte Carlo method for weakly ionized flows around reentry vehicles are presented. For ionization and recombination reactions, expressions for the model dependence of the reaction probability on velocities and energies of reagents are derived. An algorithm of dissociative recombination is presented, whose computational efficiency is reached by bypassing the modeling of the interaction of electrons and heavy particles. An approach to the construction of a weighting scheme for elastic collisions and chemical reactions is described, which significantly increases the computational efficiency of the algorithm. An example of using these numerical models and procedures for studying a weakly ionized flow around a reentry capsule under typical reentry co-nditions is given. The computation results are compared to plasma parameters measured in flight experiments.
{"title":"Application of Weighting Direct Simulation Monte Carlo Schemes to Weakly Ionized Rarefied Gas Flows","authors":"A. A. Shevyrin, Ye. A. Bondar","doi":"10.1134/s0965542524700726","DOIUrl":"https://doi.org/10.1134/s0965542524700726","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Procedures of the Direct Simulation Monte Carlo method for weakly ionized flows around reentry vehicles are presented. For ionization and recombination reactions, expressions for the model dependence of the reaction probability on velocities and energies of reagents are derived. An algorithm of dissociative recombination is presented, whose computational efficiency is reached by bypassing the modeling of the interaction of electrons and heavy particles. An approach to the construction of a weighting scheme for elastic collisions and chemical reactions is described, which significantly increases the computational efficiency of the algorithm. An example of using these numerical models and procedures for studying a weakly ionized flow around a reentry capsule under typical reentry co-nditions is given. The computation results are compared to plasma parameters measured in flight experiments.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700581
L. A. Beklaryan, A. L. Beklaryan
Abstract
The dualism of the theories of soliton solutions and solutions to functional differential equations of pointwise type is discussed. We describe the foundations underlying the formalism of this dualism, the central element of which is the concept of a soliton bouquet, as well as a dual pair “function–operator.” Within the framework of this approach, it is possible to describe the entire space of soliton solutions with a given characteristic and their asymptotics in both space and time. As an example, the model of traffic flow on the Manhattan lattice is used to describe the whole family of bounded soliton solutions.
{"title":"Dualism in the Theory of Soliton Solutions","authors":"L. A. Beklaryan, A. L. Beklaryan","doi":"10.1134/s0965542524700581","DOIUrl":"https://doi.org/10.1134/s0965542524700581","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The dualism of the theories of soliton solutions and solutions to functional differential equations of pointwise type is discussed. We describe the foundations underlying the formalism of this dualism, the central element of which is the concept of a soliton bouquet, as well as a dual pair “function–operator.” Within the framework of this approach, it is possible to describe the entire space of soliton solutions with a given characteristic and their asymptotics in both space and time. As an example, the model of traffic flow on the Manhattan lattice is used to describe the whole family of bounded soliton solutions.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700751
M. Arshad, S. Khan, M. Sohail, H. Khan, F. Tchier, M. K. Haidary, M. Nadeem
Abstract
In this paper, the mathematical model of heat and porous media equations being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional heat transfer and porous media equations. For this reason, a few examples are presented to understand the fractional heat transfer and porous media equations in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches, where partial differential equations are considered with fractional derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The obtained results are presented through tables and graphs and the approximate results are found in great contact with exact solutions.
{"title":"The Solution Comparison of Fractional Heat Transfer and Porous Media Equations Using Analytical Techniques","authors":"M. Arshad, S. Khan, M. Sohail, H. Khan, F. Tchier, M. K. Haidary, M. Nadeem","doi":"10.1134/s0965542524700751","DOIUrl":"https://doi.org/10.1134/s0965542524700751","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, the mathematical model of heat and porous media equations being considered in fractional form. The Laplace residual power series method and the Laplace Adomian decomposition technique are used to compare the solutions of the fractional heat transfer and porous media equations. For this reason, a few examples are presented to understand the fractional heat transfer and porous media equations in its more accurate form. The results show the simple and sophisticated procedures of the two proposed analytical approaches, where partial differential equations are considered with fractional derivatives. The outcomes of the described methods demonstrate that they have an accurate algorithm to construct with exceptionally precise cost calculation capabilities. The obtained results are presented through tables and graphs and the approximate results are found in great contact with exact solutions.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01DOI: 10.1134/s0965542524700635
V. N. Chugunov, Kh. D. Ikramov
Abstract
In an earlier publication of these authors, a unified approach was proposed to the construction of matrix pairs ((T,H)) that solve the (sigma )-commutation problem for Toeplitz and Hankel matrices. Here, this approach is applied for deriving new classes of solutions.
{"title":"New Classes of Solutions of the σ-Commutation Problem ( $$sigma ne 0,; pm 1$$ ) for Toeplitz and Hankel Matrices within a Unified Approach","authors":"V. N. Chugunov, Kh. D. Ikramov","doi":"10.1134/s0965542524700635","DOIUrl":"https://doi.org/10.1134/s0965542524700635","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In an earlier publication of these authors, a unified approach was proposed to the construction of matrix pairs <span>((T,H))</span> that solve the <span>(sigma )</span>-commutation problem for Toeplitz and Hankel matrices. Here, this approach is applied for deriving new classes of solutions.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-18DOI: 10.1134/s0965542524700416
A. I. Zadorin
Abstract
Numerical differentiation of functions with large gradients is considered. It is assumed that the original function of one variable can be decomposed into the sum of a regular component with bounded derivatives up to a certain order and a boundary layer component, which has large gradients and is known up to a factor. In particular, this decomposition is relevant for solution of a singularly perturbed boundary value problem, since the application of classical polynomial formulas of numerical differentiation to functions with large gradients can lead to significant errors. The error of numerical differentiation formulas is estimated for constructed formulas exact on the boundary layer component of the original function. The results of numerical experiments, consistent with the error estimates obtained, are presented.
{"title":"Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer","authors":"A. I. Zadorin","doi":"10.1134/s0965542524700416","DOIUrl":"https://doi.org/10.1134/s0965542524700416","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Numerical differentiation of functions with large gradients is considered. It is assumed that the original function of one variable can be decomposed into the sum of a regular component with bounded derivatives up to a certain order and a boundary layer component, which has large gradients and is known up to a factor. In particular, this decomposition is relevant for solution of a singularly perturbed boundary value problem, since the application of classical polynomial formulas of numerical differentiation to functions with large gradients can lead to significant errors. The error of numerical differentiation formulas is estimated for constructed formulas exact on the boundary layer component of the original function. The results of numerical experiments, consistent with the error estimates obtained, are presented.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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