José R. Galo, I. Albarreal, M. Calzada, J. Cruz, E. Fernández-Cara, Mercedes Marín
We analyze a parallel fractional step method for the solution oflinear parabolic systems. It can be viewed as a parallelization ofthe well-known θ-scheme. We perform an analysisof the convergence and stability of the scheme and we also studythe optimal choice of the parameters. We present some numericalresults corresponding to the solution of the classical heatequation.
{"title":"Stability and convergence of a parallel fractional step method forthe solution of linear parabolic problems","authors":"José R. Galo, I. Albarreal, M. Calzada, J. Cruz, E. Fernández-Cara, Mercedes Marín","doi":"10.1155/AMRX.2005.117","DOIUrl":"https://doi.org/10.1155/AMRX.2005.117","url":null,"abstract":"We analyze a parallel fractional step method for the solution oflinear parabolic systems. It can be viewed as a parallelization ofthe well-known θ-scheme. We perform an analysisof the convergence and stability of the scheme and we also studythe optimal choice of the parameters. We present some numericalresults corresponding to the solution of the classical heatequation.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"29 1","pages":"117-142"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86751917","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}
We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
{"title":"On a class of degenerate parabolic equations of Kolmogorov type","authors":"M. D. Francesco, A. Pascucci","doi":"10.1155/AMRX.2005.77","DOIUrl":"https://doi.org/10.1155/AMRX.2005.77","url":null,"abstract":"We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"30 1","pages":"77-116"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77342900","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}
For penalty approaches, it is extremely difficult to choose penalty parameter and penalty term to avoid ill-conditions. In this work, penalty techniques fornonlinear programming problems are revisited. A new penalty approach, which is called self-adaptive penalty method, is proposed. When penalty parameter and penalty term are considered, we adjust them according to the feedback information at each step (and the previous steps) in the new method so that the second information of the subproblem may be a semidefinite positive matrix whose conditioned number is not too large.
{"title":"A self-adaptive penalty approach for nonlinear programming","authors":"P. Nie","doi":"10.1155/AMRX.2005.1","DOIUrl":"https://doi.org/10.1155/AMRX.2005.1","url":null,"abstract":"For penalty approaches, it is extremely difficult to choose penalty parameter and penalty term to avoid ill-conditions. In this work, penalty techniques fornonlinear programming problems are revisited. A new penalty approach, which is called self-adaptive penalty method, is proposed. When penalty parameter and penalty term are considered, we adjust them according to the feedback information at each step (and the previous steps) in the new method so that the second information of the subproblem may be a semidefinite positive matrix whose conditioned number is not too large.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"88 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84312583","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}
This paper deals with the value iteration algorithm (VIA) for average cost Markov decision processes in Borel state and action spaces. The costs may have neither upper nor lower bounds, instead of the case of nonnegative (or bounded below) costs widely used in the previous literature. We propose aset of conditions which is weaker than those in the previous literature. Under these conditions, we first establish the average cost optimality equation. Then under an additional condition, we show that the VIA yields the optimal (minimum) average cost, anaverage optimal stationary policy, and a solution to the average cost optimality equation. Finally, we use an example to illustrate our conditions.
{"title":"Value iteration for average cost Markov decision processes inBorel spaces","authors":"Quanxin Zhu, Xianping Guo","doi":"10.1155/AMRX.2005.61","DOIUrl":"https://doi.org/10.1155/AMRX.2005.61","url":null,"abstract":"This paper deals with the value iteration algorithm (VIA) for average cost Markov decision processes in Borel state and action spaces. The costs may have neither upper nor lower bounds, instead of the case of nonnegative (or bounded below) costs widely used in the previous literature. We propose aset of conditions which is weaker than those in the previous literature. Under these conditions, we first establish the average cost optimality equation. Then under an additional condition, we show that the VIA yields the optimal (minimum) average cost, anaverage optimal stationary policy, and a solution to the average cost optimality equation. Finally, we use an example to illustrate our conditions.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"1 1","pages":"61-76"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77590122","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}
L. A. R. D. Santana, Yu.N. Bozhkov, W. C. Ferreira
We analyze mathematical models describing the behavior of populations in spatially heterogeneous environments whose most and least favourable regions for the development of the species alternate in small length scales compared to the dimensions ofrefuge candidate regions. We use homogenization methods and obtain a partial differential equation with constant coefficients. This allows us to study the survival or extinction of a population in a simpler way than performing a direct analysis of the original models in terms of differential equations involving rapidly varying coefficients.
{"title":"Multiscale methods and survival criteria for diffusive species in striped patterns","authors":"L. A. R. D. Santana, Yu.N. Bozhkov, W. C. Ferreira","doi":"10.1155/AMRX.2005.11","DOIUrl":"https://doi.org/10.1155/AMRX.2005.11","url":null,"abstract":"We analyze mathematical models describing the behavior of populations in spatially heterogeneous environments whose most and least favourable regions for the development of the species alternate in small length scales compared to the dimensions ofrefuge candidate regions. We use homogenization methods and obtain a partial differential equation with constant coefficients. This allows us to study the survival or extinction of a population in a simpler way than performing a direct analysis of the original models in terms of differential equations involving rapidly varying coefficients.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"81 1","pages":"11-37"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90389422","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}
It has long been known that the effect of a suitable magnetic field on an electrically conducting fluid controls the growth of a boundary layer. This is a recognized tool even on an industrial scale for handling highly conductive materials like liquid metals and semiconducting melts. But it is to be noted that fluids of low electrical conductivity like seawater also permit electromagnetic flow control. A considerable amount of research has been devoted to the control of flow separation as separation of flow is considered an undesirablefeature.Besidesthecontrolexercisedbyelectromagneticforces,therearetechniques like suction,blowing,and wall movement for the control of separation. A renewed interestintheuseofelectromagnetic forcestocontroltheflowofelectrolytes aroseinthe 90s. For an incompressible viscous and electrically conducting fluid flowing over a semi-infinite flat plate in the presence of a normal magnetic field, Rossow [24] has shown that the resulting boundary-layer thickness is constant far from the leading edge, whereas without the magnetic field, the thickness increases as the square root of this distance from the leading edge of the plate. The effect of such a magnetic field in a region of rising pressure would be to diminish the latter’s effect so that in cases where separation occurs, the position of the separation point is delayed; indeed if the field is sufficiently strong, separation is completely inhibited. These conclusions are confirmed experimentally by Tsinober et al. [30] who reported a downstream shift of the separation point at
{"title":"Incompressible Conducting Flow in an Applied Magnetic Field at Large Interaction Parameters","authors":"T. Sekhar, R. Sivakumar, T. Kumar","doi":"10.1155/AMRX.2005.229","DOIUrl":"https://doi.org/10.1155/AMRX.2005.229","url":null,"abstract":"It has long been known that the effect of a suitable magnetic field on an electrically conducting fluid controls the growth of a boundary layer. This is a recognized tool even on an industrial scale for handling highly conductive materials like liquid metals and semiconducting melts. But it is to be noted that fluids of low electrical conductivity like seawater also permit electromagnetic flow control. A considerable amount of research has been devoted to the control of flow separation as separation of flow is considered an undesirablefeature.Besidesthecontrolexercisedbyelectromagneticforces,therearetechniques like suction,blowing,and wall movement for the control of separation. A renewed interestintheuseofelectromagnetic forcestocontroltheflowofelectrolytes aroseinthe 90s. For an incompressible viscous and electrically conducting fluid flowing over a semi-infinite flat plate in the presence of a normal magnetic field, Rossow [24] has shown that the resulting boundary-layer thickness is constant far from the leading edge, whereas without the magnetic field, the thickness increases as the square root of this distance from the leading edge of the plate. The effect of such a magnetic field in a region of rising pressure would be to diminish the latter’s effect so that in cases where separation occurs, the position of the separation point is delayed; indeed if the field is sufficiently strong, separation is completely inhibited. These conclusions are confirmed experimentally by Tsinober et al. [30] who reported a downstream shift of the separation point at","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"55 1","pages":"229-248"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82169823","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}
We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a “good” degree reduction of a Beziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bezier curve approximation within adistance O(n −1/2 ) from the given points, where n does notdepend on r.
{"title":"On a Modified Durrmeyer-Bernstein Operator and Applications","authors":"Germain E. Randriambelosoa","doi":"10.1155/AMRX.2005.169","DOIUrl":"https://doi.org/10.1155/AMRX.2005.169","url":null,"abstract":"We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a “good” degree reduction of a Beziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bezier curve approximation within adistance O(n −1/2 ) from the given points, where n does notdepend on r.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"27 1","pages":"169-182"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82420881","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 : 2004-01-01DOI: 10.1155/S168712000402009X
S. Stefanov
We consider the problem of minimizing a convex quadratic function over a region defined by a linear equality or inequality constraint and two-sided bounds on the variables (box constraints) in R n . Such problems are interesting from both theoretical and practical points of view because they arise as subproblems of some mathematical programming problems as well as in various practical problems. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.
{"title":"Convex Quadratic Minimization Subject to a Linear Constraint and Box Constraints","authors":"S. Stefanov","doi":"10.1155/S168712000402009X","DOIUrl":"https://doi.org/10.1155/S168712000402009X","url":null,"abstract":"We consider the problem of minimizing a convex quadratic function over a region defined by a linear equality or inequality constraint and two-sided bounds on the variables (box constraints) in R n . Such problems are interesting from both theoretical and practical points of view because they arise as subproblems of some mathematical programming problems as well as in various practical problems. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"7 1","pages":"17-42"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83024046","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 : 2004-01-01DOI: 10.1155/S1687120004020052
A. Lew, P. Neff, D. Sulsky, M. Ortiz
We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.
{"title":"Optimal BV estimates for a discontinuous Galerkin method for linear elasticity","authors":"A. Lew, P. Neff, D. Sulsky, M. Ortiz","doi":"10.1155/S1687120004020052","DOIUrl":"https://doi.org/10.1155/S1687120004020052","url":null,"abstract":"We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"425 1","pages":"73-106"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78172356","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 : 2004-01-01DOI: 10.1155/S1687120004020155
M. Hadizadeh, A. R. Zokayi, P. Darania
This paper presents an account of the fundamentals of the discrete group approach for analysis and integration of practical nonlinear ordinary differential equations. In this paper, by means of appropriate transformations of discrete group analysis, some classes of second-order differential equations of Emden-Fowler type is transformed into the other solvable class. For this purpose, we give some applicable relations between the Emden-Fowler and Lane-Emden equations, in order to solve some classes of Emden-Fowler equations. This approach is effective in finding a great number of new integrable equations which thus far could not be integrated using the classical methods.
{"title":"On the discrete group analysis for solving some classes of Emden-Fowler equations","authors":"M. Hadizadeh, A. R. Zokayi, P. Darania","doi":"10.1155/S1687120004020155","DOIUrl":"https://doi.org/10.1155/S1687120004020155","url":null,"abstract":"This paper presents an account of the fundamentals of the discrete group approach for analysis and integration of practical nonlinear ordinary differential equations. In this paper, by means of appropriate transformations of discrete group analysis, some classes of second-order differential equations of Emden-Fowler type is transformed into the other solvable class. For this purpose, we give some applicable relations between the Emden-Fowler and Lane-Emden equations, in order to solve some classes of Emden-Fowler equations. This approach is effective in finding a great number of new integrable equations which thus far could not be integrated using the classical methods.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"65 1","pages":"169-178"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75195951","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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