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USSR Computational Mathematics and Mathematical Physics最新文献

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The asymptotic forms of the solution of a non-linear problem for a singularly perturbed system of diffusion-sorption equations 一类奇异摄动扩散-吸收方程组非线性问题解的渐近形式
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90049-X
A.V. Nesterov
{"title":"The asymptotic forms of the solution of a non-linear problem for a singularly perturbed system of diffusion-sorption equations","authors":"A.V. Nesterov","doi":"10.1016/0041-5553(90)90049-X","DOIUrl":"10.1016/0041-5553(90)90049-X","url":null,"abstract":"<div><p>An asymptotic expansion is constructed to solve a boundary-value problem for a singularly perturbed system of non-linear differential equations of the diffusion-sorption type.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 99-102"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90049-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"102881852","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}
引用次数: 0
Monotonization of a family of implicit schemes 一类隐式格式的单调化
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90186-V
V.I. Pinchukov
{"title":"Monotonization of a family of implicit schemes","authors":"V.I. Pinchukov","doi":"10.1016/0041-5553(90)90186-V","DOIUrl":"10.1016/0041-5553(90)90186-V","url":null,"abstract":"<div><p>An algorithm is proposed for monotonizing the correction of implicit schemes with high order of approximation of the space derivatives. The transport equation with one space variable is used as an example to prove that the corrected schemes are indeed monotone, provided that the time-step is restricted.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 3","pages":"Pages 23-28"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90186-V","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87583886","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}
引用次数: 0
A method of solving Fokker-Planck kinetic equations for a plasma 求解等离子体Fokker-Planck动力学方程的方法
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90209-B
V.N. Novikov
{"title":"A method of solving Fokker-Planck kinetic equations for a plasma","authors":"V.N. Novikov","doi":"10.1016/0041-5553(90)90209-B","DOIUrl":"10.1016/0041-5553(90)90209-B","url":null,"abstract":"<div><p>A method of solving Fokker-Planck plasma equations based on transformations to special non-stationary curvilinear coordinate systems where the resulting equations have no mixed derivatives is described.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 3","pages":"Pages 198-206"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90209-B","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91199809","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}
引用次数: 1
An economical method for computing unsteady temporally non-local radiation conditions for waveguide systems 计算波导系统非定常时非局部辐射条件的经济方法
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90066-2
A.R. Maikov, A.D. Poyezd, S.A. Yakunin
{"title":"An economical method for computing unsteady temporally non-local radiation conditions for waveguide systems","authors":"A.R. Maikov,&nbsp;A.D. Poyezd,&nbsp;S.A. Yakunin","doi":"10.1016/0041-5553(90)90066-2","DOIUrl":"https://doi.org/10.1016/0041-5553(90)90066-2","url":null,"abstract":"<div><p>An account is given of exact temporally non-local unsteady partial radiation conditions for half-open waveguide systems and an analysis is carried out. These conditions may be implemented in the discrete case by a method of temporal macrosteps, which enables one to store in the computer memory at most a fixed number of harmonics of one of the electric field components from the previous time levels. The efficiency of the method is demonstrated through a number of model problems.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 213-216"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90066-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91684366","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}
引用次数: 0
Approximation of bounded solutions and exponential dichotomy on an axis 轴上有界解的逼近和指数二分法
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90106-3
D.S. Dzhumabayev
{"title":"Approximation of bounded solutions and exponential dichotomy on an axis","authors":"D.S. Dzhumabayev","doi":"10.1016/0041-5553(90)90106-3","DOIUrl":"10.1016/0041-5553(90)90106-3","url":null,"abstract":"<div><p>Lyapunov transformations possessing certain properties are used to construct regular two-point boundary-value problems as approximations to the problem of determining a bounded solution in the general case. The concept of “limiting solutions as <em>t</em>→∞” is defined and the behaviour of solutions of linear ordinary differential equations as <em>t</em>→∞ is investigated. The necessary and sufficient conditions are derived under which a singular boundary-value problem with conditions assigned at infinity is uniquely solvable, and an appropriate approximating problem is constructed.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 6","pages":"Pages 32-43"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90106-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83388601","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}
引用次数: 1
Onsager reciprocal relationships for the motion of a rarified monatomic gas in an external field 稀薄单原子气体在外场中运动的Onsager互反关系
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90033-O
F.M. Sharipov
{"title":"Onsager reciprocal relationships for the motion of a rarified monatomic gas in an external field","authors":"F.M. Sharipov","doi":"10.1016/0041-5553(90)90033-O","DOIUrl":"10.1016/0041-5553(90)90033-O","url":null,"abstract":"<div><p>A procedure is proposed for selecting the kinetic coefficients which satisfy the Onsager reciprocal relationships in the case of the motion of a mixture of monatomic gases in a spatial domain of arbitrary shape under quite general boundary conditions. The procedure is demonstrated using two problems as examples: the motion of a gas in a short planar channel and the flow of a gas round a solid particle.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 226-231"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90033-O","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84766396","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}
引用次数: 0
The use of special transformations in the numerical solution of boundary-layer problems 特殊变换在边界层问题数值解中的应用
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90006-E
V.D. Liseikin
{"title":"The use of special transformations in the numerical solution of boundary-layer problems","authors":"V.D. Liseikin","doi":"10.1016/0041-5553(90)90006-E","DOIUrl":"10.1016/0041-5553(90)90006-E","url":null,"abstract":"<div><p>Estimates of the derivatives are obtained for certain boundary-layer problems, making it possible to isolate singularities of the solutions effectively. On the basis of these estimates special transformations, which smooth out the singularities, are constructed. These transformations are used to construct numerical algorithms for solving certain problems in which the coefficient of the highest-order derivative is a small parameter. It is proved that the numerical solution converges uniformly to the exact solution.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 43-53"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90006-E","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80339868","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}
引用次数: 11
The features of gradient methods for distributed optimal-control problems 分布最优控制问题的梯度方法的特点
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90002-A
V.I. Sumin
{"title":"The features of gradient methods for distributed optimal-control problems","authors":"V.I. Sumin","doi":"10.1016/0041-5553(90)90002-A","DOIUrl":"10.1016/0041-5553(90)90002-A","url":null,"abstract":"<div><p>A wide class of nonlinear distributed control systems is distinguished for which the Frechet differentiability in spaces of the type <em>L</em><sub>∞</sub> of functionals of fairly general form is proved for arbitrary orders of increase of the “right-hand sides” with respect to the “phase” and controlling variables. Formulas are obtained for the corresponding Frechet derivatives, which can be effectively used when validating methods of descent of the gradient type in optimal-control problems with a limited set of permissible values of the control. Central to this is the theorem of the sufficient conditions of stability (with respect to perturbation of the control) of the existence of global solutions of systems of the distinguished class. Specific examples are given.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 1","pages":"Pages 1-15"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90002-A","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85531469","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}
引用次数: 32
Difference methods in problems of the optimal control of the steady selfaction of light beams 光束自稳态最优控制问题的差分方法
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90055-W
M.M. Potapov, A.V. Razgulin
{"title":"Difference methods in problems of the optimal control of the steady selfaction of light beams","authors":"M.M. Potapov,&nbsp;A.V. Razgulin","doi":"10.1016/0041-5553(90)90055-W","DOIUrl":"10.1016/0041-5553(90)90055-W","url":null,"abstract":"<div><p>A discussion is presented of optimization problems arising in the simulation of the propagation of optical radiation in a material medium with different regimes of absorption and field selfaction. Estimates are established for the rate of convergence of difference and projection-difference schemes for the appropriate non-linear differential equations, no prior assumptions being made as to the smoothness of the generalized solutions or compatability conditions for the grid step-sizes. Estimates are also obtained for the rate of convergence of the finite-dimensional approximations to the optimal control problems based on these schemes.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 134-142"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90055-W","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74614954","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}
引用次数: 3
Some properties of discrete fuzzy sets 离散模糊集的若干性质
USSR Computational Mathematics and Mathematical Physics Pub Date : 1990-01-01 Epub Date: 2004-04-01 DOI: 10.1016/0041-5553(90)90050-3
M.F. Kaspshitskaya, I.V. Sergienko, A.I. Stiranka
{"title":"Some properties of discrete fuzzy sets","authors":"M.F. Kaspshitskaya,&nbsp;I.V. Sergienko,&nbsp;A.I. Stiranka","doi":"10.1016/0041-5553(90)90050-3","DOIUrl":"10.1016/0041-5553(90)90050-3","url":null,"abstract":"<div><p>Discrete fuzzy sets and a possible method of defining metrics on them are considered. The proposed method is based on the concept of quasisupport functions given below, and is more general than those described previously. A range of assertions concerning the properties of quasisupport functions of combinational fuzzy sets is also given.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 103-107"},"PeriodicalIF":0.0,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0041-5553(90)90050-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75412162","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}
引用次数: 2
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