Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.2.10
V. Matvienko, V. V. Pichkur, D. Cherniy, E. O. Demkivskiy
The paper analyzes the mathematical problem consisting of constructing a general solution to the problem of terminal control of a discrete system. We gibe the general solution and the general pseudosolution for the linear system. A solution to the problem of constructing the reachability set from the origin of the coordinates with restrictions on the norm of the control function is obtained.
{"title":"GENERAL SOLUTION OF TERMINAL CONTROL PROBLEM OF A LINEAR DISCRETE SYSTEM","authors":"V. Matvienko, V. V. Pichkur, D. Cherniy, E. O. Demkivskiy","doi":"10.17721/2706-9699.2022.2.10","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.10","url":null,"abstract":"The paper analyzes the mathematical problem consisting of constructing a general solution to the problem of terminal control of a discrete system. We gibe the general solution and the general pseudosolution for the linear system. A solution to the problem of constructing the reachability set from the origin of the coordinates with restrictions on the norm of the control function is obtained.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"85 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80324544","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}
Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.1.02
V. A. Kolesnykov
The article is dedicated to the Richards–Klute equation. A derivation of this equation and several forms of its notation are given. Analytical methods for solving the equation are analyzed. The current state and directions of theoretical research are described. The main numerical methods for solving the equation are presented and the methods of time and space discretization used in them are analyzed. The list of programs for numerical modeling of the Richards– Klute equation is given. Their comparative analysis was carried out. Possible areas of further research are mentioned.
{"title":"RICHARDS–KLUTE EQUATION: THE STATE OF THE ART","authors":"V. A. Kolesnykov","doi":"10.17721/2706-9699.2022.1.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.02","url":null,"abstract":"The article is dedicated to the Richards–Klute equation. A derivation of this equation and several forms of its notation are given. Analytical methods for solving the equation are analyzed. The current state and directions of theoretical research are described. The main numerical methods for solving the equation are presented and the methods of time and space discretization used in them are analyzed. The list of programs for numerical modeling of the Richards– Klute equation is given. Their comparative analysis was carried out. Possible areas of further research are mentioned.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84645100","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}
Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.1.03
E. Namgalauri, O. Purtukhia
In this work, we study the issues of a constructive stochastic integral representation of Brownian functionals, which are interesting from the point of view of their practical application in the problem of hedging a European option. In addition to briefly discussing known results in this direction, in the case of stochastically smooth (in Malliavin sense) functionals, we also illustrate the usefulness of the Glonti–Purtukhia representation for non-smooth functionals. In particular, we generalize the Clarke–Ocone formula to the case when the functional is not stochastically smooth, but its conditional mathematical expectation is stochastically differentiable, and find an explicit expression for the integrand. Moreover, we consider such functionals that do not satisfy even weakened conditions, that is, non-smooth, past-dependent Brownian functionals, the conditional mathematical expectations of which are also not stochastically differentiable, and again we give a constructive martingale representation.
{"title":"DIFFERENT APPROACHES IN THE CONSTRUCTIVE MARTINGALE REPRESENTATION OF BROWNIAN FUNCTIONALS","authors":"E. Namgalauri, O. Purtukhia","doi":"10.17721/2706-9699.2022.1.03","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.03","url":null,"abstract":"In this work, we study the issues of a constructive stochastic integral representation of Brownian functionals, which are interesting from the point of view of their practical application in the problem of hedging a European option. In addition to briefly discussing known results in this direction, in the case of stochastically smooth (in Malliavin sense) functionals, we also illustrate the usefulness of the Glonti–Purtukhia representation for non-smooth functionals. In particular, we generalize the Clarke–Ocone formula to the case when the functional is not stochastically smooth, but its conditional mathematical expectation is stochastically differentiable, and find an explicit expression for the integrand. Moreover, we consider such functionals that do not satisfy even weakened conditions, that is, non-smooth, past-dependent Brownian functionals, the conditional mathematical expectations of which are also not stochastically differentiable, and again we give a constructive martingale representation.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74323580","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}
Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.2.20
Vsevolod Bohaienko, A. Gladky
The paper studies the performance of multithreaded parallel implementation of a finite-difference solver for a two-dimensional space-fractional generalization of Richards equation. For numerical solution we used implicit Crank-Nicholson scheme with L1-approximation of Caputo fractional derivative and TFQMR linear systems’ solver. OpenMP implementation was tested on three CPUs — server Intel Xeon Bronze 3104 and AMD EPYC 7542 along with laptop AMD Ryzen 3 5300U. Testing results show that the proposed implementation can give close-to-linear acceleration when executing on up to 8 cores. On high-performance AMD EPYC maximal acceleration was achieved when 32-64 cores were used showing limited scalability of the algorithms on such a CPU.
{"title":"MULTITHREADING PERFORMANCE SIMULATING FRACTIONAL-ORDER MOISTURE TRANSPORT ON AMD EPYC","authors":"Vsevolod Bohaienko, A. Gladky","doi":"10.17721/2706-9699.2022.2.20","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.20","url":null,"abstract":"The paper studies the performance of multithreaded parallel implementation of a finite-difference solver for a two-dimensional space-fractional generalization of Richards equation. For numerical solution we used implicit Crank-Nicholson scheme with L1-approximation of Caputo fractional derivative and TFQMR linear systems’ solver. OpenMP implementation was tested on three CPUs — server Intel Xeon Bronze 3104 and AMD EPYC 7542 along with laptop AMD Ryzen 3 5300U. Testing results show that the proposed implementation can give close-to-linear acceleration when executing on up to 8 cores. On high-performance AMD EPYC maximal acceleration was achieved when 32-64 cores were used showing limited scalability of the algorithms on such a CPU.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85466607","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}
Pub Date : 2021-07-21DOI: 10.17721/2706-9699.2021.1.21
A. V. Menshykov, V. Menshykov, O. Kladova
Solution of the problem for an interface crack under the action of a harmonic shear wave is presented. It is shown that the same problems solutions of other authors were performed without taking into account the crack faces contact, and results obtained indicate the interpenetration of the faces, that is not possible. Thus, it is proved that the problem is nonlinear because the positions and sizes of the contact zone are unknown and variable during the loading. The solution is obtained by the boundary integral equations method taking into account the contact interaction of the crack faces: using the Somigliana dynamic identity and the boundary equations arising from them, the transition from the two-dimensional problem to the equivalent problem at the boundaries of the domain is realized; the vector components in the boundary integral equations are presented by Fourier series, to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone the Signorini unilateral constraints are involved. The numerical solution is performed by the method of boundary elements with constant approximation of the problem parameters on an element. Numerical researches of the shear wave frequency influence onto the crack faces and adjoining surface displacements, opening and extent of crack faces contact zone are carried out. The quantitative difference between the maximum tangential and normal components of adhesion line and the crack faces displacements is shown. It is shown that the position and length of the contact area change during the load period, and the magnitudes of the contact forces vary along the crack length.
{"title":"NONLINEAR PROBLEM OF INTERFACE CRACK BEHAVIOR UNDER THE ACTION OF SHEARING WAVE","authors":"A. V. Menshykov, V. Menshykov, O. Kladova","doi":"10.17721/2706-9699.2021.1.21","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.21","url":null,"abstract":"Solution of the problem for an interface crack under the action of a harmonic shear wave is presented. It is shown that the same problems solutions of other authors were performed without taking into account the crack faces contact, and results obtained indicate the interpenetration of the faces, that is not possible. Thus, it is proved that the problem is nonlinear because the positions and sizes of the contact zone are unknown and variable during the loading. The solution is obtained by the boundary integral equations method taking into account the contact interaction of the crack faces: using the Somigliana dynamic identity and the boundary equations arising from them, the transition from the two-dimensional problem to the equivalent problem at the boundaries of the domain is realized; the vector components in the boundary integral equations are presented by Fourier series, to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone the Signorini unilateral constraints are involved. The numerical solution is performed by the method of boundary elements with constant approximation of the problem parameters on an element. Numerical researches of the shear wave frequency influence onto the crack faces and adjoining surface displacements, opening and extent of crack faces contact zone are carried out. The quantitative difference between the maximum tangential and normal components of adhesion line and the crack faces displacements is shown. It is shown that the position and length of the contact area change during the load period, and the magnitudes of the contact forces vary along the crack length.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"67 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90608782","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.2.05
A. Kosolap
This article provides an analysis the practical effectiveness of the method of exact quadratic regularization. Significant computational experiments have been performed to solve the complex multi-modal test and practical problems. The results of computational experiments are compared with the best results obtained by existing methods of global optimization. Comparative analysis shows a much greater practical efficiency of the method of exact quadratic regularization.
{"title":"PRACTICAL EFFICIENCY OF EQR METHOD FOR SOLVING GLOBAL OPTIMIZATION PROBLEMS","authors":"A. Kosolap","doi":"10.17721/2706-9699.2021.2.05","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.2.05","url":null,"abstract":"This article provides an analysis the practical effectiveness of the method of exact quadratic regularization. Significant computational experiments have been performed to solve the complex multi-modal test and practical problems. The results of computational experiments are compared with the best results obtained by existing methods of global optimization. Comparative analysis shows a much greater practical efficiency of the method of exact quadratic regularization.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"604 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85334621","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.14
Shota Rustaveli, state university, Geórgia, E-mail ibraimd
The methodology of neural networks is even more often applied in tasks of management and decision-making, including in the sphere of trade and finance. The basis of neural networks is made by nonlinear adaptive systems which proved the efficiency at the solution of problems of forecasting.
{"title":"TRAINING OF ARTIFICIAL NEURAL NETWORK","authors":"Shota Rustaveli, state university, Geórgia, E-mail ibraimd","doi":"10.17721/2706-9699.2021.1.14","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.14","url":null,"abstract":"The methodology of neural networks is even more often applied in tasks of management and decision-making, including in the sphere of trade and finance. The basis of neural networks is made by nonlinear adaptive systems which proved the efficiency at the solution of problems of forecasting.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"59 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84081787","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}
An original approach for dividing the reaction of a viscoelastic support into inertial, viscous and elastic components is proposed to assess the effect of various characteristics of additional supports on the deformed state of structural elements. The effectiveness of the proposed approach was tested for a mechanical system consisting of a rectangular isotropic plate of medium thickness, hinged-supported along the contour, and an additional concentrated viscoelastic support, taking into account its mass-inertial characteristics. The deformation of the plate is considered within the framework of Timoshenko's hypotheses. Vibrations of the plate are caused by the applying of an external non-stationary loading. The influence of the additional support is modeled by three independent non-stationary concentrated forces. The paper presents the main analytical relations for obtaining a system of three integral Volterra equations, which is solved numerically and analytically. After performing discretization in time, the system of integral equations is transformed into a system of matrix equations. The resulting system of matrix equations is solved using the generalized Cramer algorithm for block matrices and the Tikhonov regularization method. We point out that the material described is applicable to other objects that have additional supports (beams, plates and shells, which can have different supports along the contour and different shapes in plan). The results of a numerical experiment to determine the components (viscous, elastic and inertial) of the full reaction to the plate, arising due to the presence of an additional support, are presented. The reliability of the proposed approach is confirmed by the coincidence of the results of comparing the reactions found by two methods: numerical-analytical for one complete reaction, as in work [1], and numerical for the full reaction (obtained by adding three components).
{"title":"DIVIDING OF THE FULL REACTION OF THE ADDITIONAL SUPPORT CONTACTING WITH THE PLATE INTO VISCOUS, ELASTIC AND INERTIAL COMPONENTS","authors":"Automobile and, Highway University, E-mail voropay.","doi":"10.17721/2706-9699.2021.1.10","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.10","url":null,"abstract":"An original approach for dividing the reaction of a viscoelastic support into inertial, viscous and elastic components is proposed to assess the effect of various characteristics of additional supports on the deformed state of structural elements. The effectiveness of the proposed approach was tested for a mechanical system consisting of a rectangular isotropic plate of medium thickness, hinged-supported along the contour, and an additional concentrated viscoelastic support, taking into account its mass-inertial characteristics. The deformation of the plate is considered within the framework of Timoshenko's hypotheses. Vibrations of the plate are caused by the applying of an external non-stationary loading. The influence of the additional support is modeled by three independent non-stationary concentrated forces. The paper presents the main analytical relations for obtaining a system of three integral Volterra equations, which is solved numerically and analytically. After performing discretization in time, the system of integral equations is transformed into a system of matrix equations. The resulting system of matrix equations is solved using the generalized Cramer algorithm for block matrices and the Tikhonov regularization method. We point out that the material described is applicable to other objects that have additional supports (beams, plates and shells, which can have different supports along the contour and different shapes in plan). The results of a numerical experiment to determine the components (viscous, elastic and inertial) of the full reaction to the plate, arising due to the presence of an additional support, are presented. The reliability of the proposed approach is confirmed by the coincidence of the results of comparing the reactions found by two methods: numerical-analytical for one complete reaction, as in work [1], and numerical for the full reaction (obtained by adding three components).","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80578381","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.06
V. Voloshchuk, E. Nikiforovich
The most widespread approaches to the study of thermal systems involve the iterative implementation of the following steps: thermodynamics, heat and mass transfer, hydrodynamics, economics and ecology. Such methodology cannot combine economic, environmental and thermodynamic aspects from the beginning of the analysis. It does not provide information concerning not only external, but also internal, caused by thermodynamic inefficiencies of system components, impact factors on economic and ecological characteristics. Modeling methods based on the combined application of the First and Second Laws of Thermodynamics (methods of entropy and exergetic analysis), and their combination with economic and environmental assessment make it possible to identify the location, magnitude, causes, costs and environmental impact of thermodynamic inefficiencies in an energy conversion system. The paper proposes the improvement of methods for modeling thermal systems on the base of exergy analysis. It has been shown that combining exergetic, economic and ecological assessment can significantly simplify tasks of finding parameters and structure of the studied system. Examples of implementation of such studies have been presented.
{"title":"MODELING OF THERMAL INSTALLATIONS BASED ON THERMODYNAMIC APPROACHES","authors":"V. Voloshchuk, E. Nikiforovich","doi":"10.17721/2706-9699.2021.1.06","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.06","url":null,"abstract":"The most widespread approaches to the study of thermal systems involve the iterative implementation of the following steps: thermodynamics, heat and mass transfer, hydrodynamics, economics and ecology. Such methodology cannot combine economic, environmental and thermodynamic aspects from the beginning of the analysis. It does not provide information concerning not only external, but also internal, caused by thermodynamic inefficiencies of system components, impact factors on economic and ecological characteristics. Modeling methods based on the combined application of the First and Second Laws of Thermodynamics (methods of entropy and exergetic analysis), and their combination with economic and environmental assessment make it possible to identify the location, magnitude, causes, costs and environmental impact of thermodynamic inefficiencies in an energy conversion system. The paper proposes the improvement of methods for modeling thermal systems on the base of exergy analysis. It has been shown that combining exergetic, economic and ecological assessment can significantly simplify tasks of finding parameters and structure of the studied system. Examples of implementation of such studies have been presented.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88729903","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.22
V. Neagu
The article presents some generalizations and refinements of the article [1]: examples of integral (non-compact) operators with point wise singularities which are admissible perturbations of the Noetherian operators are constructed; a connection between the regularizes of the perturbed and original operators is established and the equality between the indices of the perturbed and the original operators is proved. The presented results are based on the formulas obtained in this paper for the composition of an operator with the Cauchy kernel and the operators with point wise singularities.
{"title":"REGULARIZATION OF SOME PERTURBED INTEGRAL OPERATORS IN THE SPACES Lp","authors":"V. Neagu","doi":"10.17721/2706-9699.2021.1.22","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.22","url":null,"abstract":"The article presents some generalizations and refinements of the article [1]: examples of integral (non-compact) operators with point wise singularities which are admissible perturbations of the Noetherian operators are constructed; a connection between the regularizes of the perturbed and original operators is established and the equality between the indices of the perturbed and the original operators is proved. The presented results are based on the formulas obtained in this paper for the composition of an operator with the Cauchy kernel and the operators with point wise singularities.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77574826","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}
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