{"title":"Chebyshev acceleration of the schwarz alternation process","authors":"S.A. Sander","doi":"10.1016/0041-5553(90)90077-6","DOIUrl":"10.1016/0041-5553(90)90077-6","url":null,"abstract":"<div><p>Chebyshev acceleration of a difference analogue of the Schwarz alternation process is considered. Estimates for the rate of convergence, in the <em>W</em><sub>2<em>h</em></sub><sup>1</sup> norm, are presented.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 2","pages":"Pages 62-67"},"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)90077-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77243136","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}
{"title":"The maximum principle residual functional in optimal control theory","authors":"M.I. Sumin","doi":"10.1016/0041-5553(90)90053-U","DOIUrl":"10.1016/0041-5553(90)90053-U","url":null,"abstract":"<div><p>The possibilities of applying results related to the so-called maximum principle residual functional to justify and design algorithms for solving optimal control problems and discussed. The differential properties of the value function of the optimal control problem are established. A dual method for solving the optimal control problem, based on maximizing the value function of a modified Lagrange functional, is described.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 117-129"},"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)90053-U","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77631730","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}
{"title":"Numerical solution of a quasilinear parabolic equation with a boundary layer","authors":"I.P. Boglayev","doi":"10.1016/0041-5553(90)90190-4","DOIUrl":"10.1016/0041-5553(90)90190-4","url":null,"abstract":"<div><p>To solve a quasilinear parabolic equation with small parameter multiplying the derivatives with respect to the spatial variables, a numerical method is constructed with an estimate of the error, which is uniform with respect to the parameter. The construction of a nonlinear difference scheme is based on the method of straight lines and on the application of exact systems to one-dimensional problems. The computational mesh is chosen so that its density increases in a suitable way in the neighbourhood of the boundary. We propose that the nonlinear scheme be solved by an iterative algorithm, which converges uniformly with respect to the small parameter.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 3","pages":"Pages 55-63"},"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)90190-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91487894","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}
{"title":"Localized compression regimes in a heat-conducting gas","authors":"V.V. Gudkov, A.P. Mikhailov, V.V. Stepanova","doi":"10.1016/0041-5553(90)90088-A","DOIUrl":"10.1016/0041-5553(90)90088-A","url":null,"abstract":"<div><p>The effect of limiting regimes with peaking on a compressible sphere with thermal conductivity <em>χ</em> = <em>χ</em><sub>0</sub><em>ρ</em><sup><em>α</em></sup><em>T</em><sup><em>β</em></sup>, <em>β</em> > 0, is examined. The investigation is carried out for selfsimilar solutions of the power type. Conditions are established for shockless supercompression of the material and joint localization of the thermal and gas-dynamic processes, which depend on the thermophysical properties of the medium and the limiting law. The phenomena are also investigated numerically.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 2","pages":"Pages 130-138"},"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)90088-A","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90575549","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}
{"title":"Decomposition in extremal problems of special structure","authors":"I.S. Litvinchev","doi":"10.1016/0041-5553(90)90041-P","DOIUrl":"10.1016/0041-5553(90)90041-P","url":null,"abstract":"<div><p>A decomposition method based on aggregated macrovariables is proposed for optimization problems in which some of the constraints have a special structure — block, block-separable, or blocks with coupling variables. A number of standard decomposition methods are derived in the proposed framework. Problems with known bounds on the coupling variables are considered.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 32-38"},"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)90041-P","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85670820","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}
{"title":"On an inertial flow","authors":"Yu.D. Shmyglevskii","doi":"10.1016/0041-5553(90)90126-D","DOIUrl":"10.1016/0041-5553(90)90126-D","url":null,"abstract":"<div><p>An example of a steady axisymmetric flow of an incompressible fluid, with a non-zero peripheral velocity component and straight streamlines, is constructed.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 6","pages":"Pages 167-168"},"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)90126-D","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"99282866","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}
{"title":"Digital simulation of evolutionary stochastic differential equations","authors":"Yu.G. Bulychev, S.A. Pogonyshev","doi":"10.1016/0041-5553(90)90056-X","DOIUrl":"10.1016/0041-5553(90)90056-X","url":null,"abstract":"<div><p>Euler, Euler-Cauchy, and Runge-Kutta difference schemes and Fast Fourier-Transform procedures are used to develop efficient methods for the digital simulation of evolutionary stochastic partial differential equations that ensure the desired computational accuracy at minimum cost. Bounds of the computation errors are given.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 143-149"},"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)90056-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73568887","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}
{"title":"On the use of hybrid grid-characteristic schemes for the numerical solution of three-dimensional problems in the dynamics of a deformable solid","authors":"I.B. Petrov, A.G. Tormasov, A.S. Kholodov","doi":"10.1016/0041-5553(90)90062-W","DOIUrl":"10.1016/0041-5553(90)90062-W","url":null,"abstract":"<div><p>The three-dimensional dynamical problem of the oblique impact of a rigid pellet on a deformable elastoplastic barrier is solved using a hybrid grid-characteristic scheme for the numerical solution of non-stationary systems of hyperbolic equations. Thegrid-characteristic hybrid scheme is adapted for the numerical solution of multidimensional non-stationary problems in the mechanics of deformable bodies.</p></div>","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 4","pages":"Pages 191-196"},"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)90062-W","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74491333","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}
{"title":"Combined recovery of the quadrupole splitting distribution function and the dependence of the isomer shift using Mössbauer spectral data","authors":"O.G. Odintsov, E.A. Pushkarev","doi":"10.1016/0041-5553(90)90168-R","DOIUrl":"10.1016/0041-5553(90)90168-R","url":null,"abstract":"","PeriodicalId":101271,"journal":{"name":"USSR Computational Mathematics and Mathematical Physics","volume":"30 5","pages":"Pages 112-115"},"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)90168-R","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74635483","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}