Pub Date : 2022-01-01DOI: 10.17721/2706-9699.2022.1.06
O. B. Stelya, D. Klyushin
The article describes a numerical method for optimizing the chemotherapy of malignant tumors on the basis of drug delivery using increased convection. The problem of optimal control with point sources for reaching the desired intratumor distribution of drugs in macroscopic scale granting the properties of intersticial space and effects of convective diffusion is considered. The efficiency of proposed algorithm for optimal control is shown.
{"title":"OPTIMIZATION OF CHEMOTHERAPY OF MALIGNANT TUMORS BASED ON DELIVERY OF DRUGS WITH ENHANCED CONVECTION","authors":"O. B. Stelya, D. Klyushin","doi":"10.17721/2706-9699.2022.1.06","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.06","url":null,"abstract":"The article describes a numerical method for optimizing the chemotherapy of malignant tumors on the basis of drug delivery using increased convection. The problem of optimal control with point sources for reaching the desired intratumor distribution of drugs in macroscopic scale granting the properties of intersticial space and effects of convective diffusion is considered. The efficiency of proposed algorithm for optimal control is shown.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81817324","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: 10.17721/2706-9699.2022.2.18
D. Khusainov, A. V. A. V. Shatyrko, Z. R. Hahurin
The paper considers the task of optimal stabilization for linear stationary differential equations. Usage of Lyapunov functions for optimal stabilization. We prove the theorem about optimal stabilization and determine the expression of optimal control for considered class of tasks.
{"title":"OPTIMAL STABILIZATION FOR DIFFERENTIAL EQUATIONS","authors":"D. Khusainov, A. V. A. V. Shatyrko, Z. R. Hahurin","doi":"10.17721/2706-9699.2022.2.18","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.18","url":null,"abstract":"The paper considers the task of optimal stabilization for linear stationary differential equations. Usage of Lyapunov functions for optimal stabilization. We prove the theorem about optimal stabilization and determine the expression of optimal control for considered class of tasks.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79000122","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: 10.17721/2706-9699.2022.2.02
A. Anikushyn, O. Zhyvolovych
In the paper we consider a Dirichlet problem for an integro-differential equation with Volterra type integral term. Proving a priori estimates for the differential and integral parts, we provide negative norms’ a priori estimates for the operator of the problem. Based on the latest, we formulate theorems regarding the well-posedness of the formulated boundary value problem.
{"title":"WELL-POSEDNESS OF A DIRICHLET PROBLEM FOR A HYPERBOLIC TYPE INTEGRO-DIFFERENTIAL EQUATION","authors":"A. Anikushyn, O. Zhyvolovych","doi":"10.17721/2706-9699.2022.2.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.02","url":null,"abstract":"In the paper we consider a Dirichlet problem for an integro-differential equation with Volterra type integral term. Proving a priori estimates for the differential and integral parts, we provide negative norms’ a priori estimates for the operator of the problem. Based on the latest, we formulate theorems regarding the well-posedness of the formulated boundary value problem.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"47 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90414024","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: 10.17721/2706-9699.2022.2.11
I. P. Moroz
An approach for the ambipolar diffusion equation boundary value problem solving, which is posed in a two-dimensional domain with oscillating boundaries, is proposed. The construction of the solution of the model problem is based on the corresponding problem for a certain internal canonical majorant domain and the methodology for constructing the so-called corrective corrections based on the use of the perturbation theory elements. A feature of this problem is that it is not the problem equation or boundary conditions that are perturbed, but the region. And this leads to the construction of a fundamentally new solution structure.
{"title":"THE CORRECTING FUNCTIONS METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR THE AMBIPOLAR DIFFUSION EQUATION IN A DOMAIN WITH A CURVILINEAR BOUNDARIES","authors":"I. P. Moroz","doi":"10.17721/2706-9699.2022.2.11","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.11","url":null,"abstract":"An approach for the ambipolar diffusion equation boundary value problem solving, which is posed in a two-dimensional domain with oscillating boundaries, is proposed. The construction of the solution of the model problem is based on the corresponding problem for a certain internal canonical majorant domain and the methodology for constructing the so-called corrective corrections based on the use of the perturbation theory elements. A feature of this problem is that it is not the problem equation or boundary conditions that are perturbed, but the region. And this leads to the construction of a fundamentally new solution structure.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"67 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87155864","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: 10.17721/2706-9699.2022.2.17
V. Sobchuk, I. O. Zelenska
We study a system with a small parameter at the highest derivatives. Using model operator Airy–Langer for defined regular function. Received the conditions of construction an uniform asymptotic solution for a given system.
{"title":"STUDY OF ASYMPTOTIC SOLUTIONS OF SYSTEMS OF SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS WITH TURNING POINTS","authors":"V. Sobchuk, I. O. Zelenska","doi":"10.17721/2706-9699.2022.2.17","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.17","url":null,"abstract":"We study a system with a small parameter at the highest derivatives. Using model operator Airy–Langer for defined regular function. Received the conditions of construction an uniform asymptotic solution for a given system.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"116 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89415365","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: 10.17721/2706-9699.2022.2.01
I. M. Aleksandrovych, S. Lyashko, V. Lyashko, N. I. Lyashko, M. Sidorov
Integral operators that transform arbitrary functions into regular solutions of hyperbolic equations of the second and higher orders are applied to solving boundary value problems. In particular, the Riquet problem for the Euler–Poisson–Darboux equation of the 4th order is posed and solved.
{"title":"RIQUET PROBLEM FOR ONE MODEL EQUATION OF THE 4TH ORDER HYPERBOLIC TYPE","authors":"I. M. Aleksandrovych, S. Lyashko, V. Lyashko, N. I. Lyashko, M. Sidorov","doi":"10.17721/2706-9699.2022.2.01","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.01","url":null,"abstract":"Integral operators that transform arbitrary functions into regular solutions of hyperbolic equations of the second and higher orders are applied to solving boundary value problems. In particular, the Riquet problem for the Euler–Poisson–Darboux equation of the 4th order is posed and solved.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87943172","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: 10.17721/2706-9699.2022.1.07
P. Stetsyuk, V. Stovba, O. Khomiak
In this paper, a mathematical model of an open twostage transportation problem and its two modifications are considered. The first modification takes into account the upper bounds of transitional points capacities, the second takes into account the possibility of selection of the fixed number of transitional points, which is less than their total number. For all three cases the necessary and sufficient conditions of constraints feasibility are substantiated. The results of the computational experiments using gurobi and cplex solvers are presented.
{"title":"TWO-STAGE TRANSPORTATION PROBLEM AND ITS TWO MODIFICATIONS","authors":"P. Stetsyuk, V. Stovba, O. Khomiak","doi":"10.17721/2706-9699.2022.1.07","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.1.07","url":null,"abstract":"In this paper, a mathematical model of an open twostage transportation problem and its two modifications are considered. The first modification takes into account the upper bounds of transitional points capacities, the second takes into account the possibility of selection of the fixed number of transitional points, which is less than their total number. For all three cases the necessary and sufficient conditions of constraints feasibility are substantiated. The results of the computational experiments using gurobi and cplex solvers are presented.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"284 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72649396","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: 10.17721/2706-9699.2022.2.08
S. Lyashko, N. I. Lyashko, D. Klyushin, A. Tymoshenko
In this paper a one-dimensional nonlinear Richards equation describing fluid flow in porous medium with inserted equalpowered sources is studied. An experimental iterational method is proposed to find source power to minimize the deviation of received humidity values from target values. Modeling was performed using numerical difference approximation of derivatives, resulting into a system of nonlinear equations with dependence from previous time step. The offered method allows to perform modeling for different source power values, and chooses the most suitable one.Iterations stop when they reach average modular difference value less than calculation error of numerical difference scheme. Here explicit scheme was used to save time, equations were tested for unsaturated medium only to avoid flooding the area, so source power is tested with given limitations. Results of simulations and choice for next source power approximations are described and compared until solution is found. This approach is considered as experimental so we plan to perform more analysis in the future.
{"title":"METHOD FOR SOURCE POWER IDENTIFICATION IN RICHARDS EQUATION","authors":"S. Lyashko, N. I. Lyashko, D. Klyushin, A. Tymoshenko","doi":"10.17721/2706-9699.2022.2.08","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.08","url":null,"abstract":"In this paper a one-dimensional nonlinear Richards equation describing fluid flow in porous medium with inserted equalpowered sources is studied. An experimental iterational method is proposed to find source power to minimize the deviation of received humidity values from target values. Modeling was performed using numerical difference approximation of derivatives, resulting into a system of nonlinear equations with dependence from previous time step. The offered method allows to perform modeling for different source power values, and chooses the most suitable one.Iterations stop when they reach average modular difference value less than calculation error of numerical difference scheme. Here explicit scheme was used to save time, equations were tested for unsaturated medium only to avoid flooding the area, so source power is tested with given limitations. Results of simulations and choice for next source power approximations are described and compared until solution is found. This approach is considered as experimental so we plan to perform more analysis in the future.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77385536","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: 10.17721/2706-9699.2022.2.15
G. Sandrakov
Models of wave processes in porous periodic media are considered. It is taken into account that the corresponding wave equations depend on small parameters characterizing the microscale, density, and permeability of such media. The algorithm for determining asymptotic expansions for these equations is given. Estimates for the accuracy of such expansions are presented.
{"title":"MODELING OF WAVE PROCESSES IN POROUS MEDIA AND ASYMPTOTIC EXPANSIONS","authors":"G. Sandrakov","doi":"10.17721/2706-9699.2022.2.15","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.15","url":null,"abstract":"Models of wave processes in porous periodic media are considered. It is taken into account that the corresponding wave equations depend on small parameters characterizing the microscale, density, and permeability of such media. The algorithm for determining asymptotic expansions for these equations is given. Estimates for the accuracy of such expansions are presented.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"69 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86961673","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: 10.17721/2706-9699.2022.2.19
D. Khusainov, A. Shatyrko, T. Shakotko, Rahima Mustafaeva
A scalar linear differential equation of the neutral type is considered. When studying the stability and obtaining estimates of the convergence of the solutions of the equation, the functional of the Lyapunov–Krasovsky form is used in the quadratic form plus the integral term. The stability conditions of the zero solution are given. Finding the parameters of the functional is reduced to an optimization problem.
{"title":"AN OPTIMIZATION APPROACH TO CONSTRUCTING LYAPUNOV–KRASOVSKY FUNCTIONALS","authors":"D. Khusainov, A. Shatyrko, T. Shakotko, Rahima Mustafaeva","doi":"10.17721/2706-9699.2022.2.19","DOIUrl":"https://doi.org/10.17721/2706-9699.2022.2.19","url":null,"abstract":"A scalar linear differential equation of the neutral type is considered. When studying the stability and obtaining estimates of the convergence of the solutions of the equation, the functional of the Lyapunov–Krasovsky form is used in the quadratic form plus the integral term. The stability conditions of the zero solution are given. Finding the parameters of the functional is reduced to an optimization problem.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74518062","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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