Boundary Value Problems for Transport Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 1461219949
Total Pages : 295 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Boundary Value Problems for Transport Equations by : Valeri Agoshkov

Download or read book Boundary Value Problems for Transport Equations written by Valeri Agoshkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern theory of boundary value problems the following ap proach to investigation is agreed upon (we call it the functional approach): some functional spaces are chosen; the statements of boundary value prob the basis of these spaces; and the solvability of lems are formulated on the problems, properties of solutions, and their dependence on the original data of the problems are analyzed. These stages are put on the basis of the correct statement of different problems of mathematical physics (or of the definition of ill-posed problems). For example, if the solvability of a prob lem in the functional spaces chosen cannot be established then, probably, the reason is in their unsatisfactory choice. Then the analysis should be repeated employing other functional spaces. Elliptical problems can serve as an example of classical problems which are analyzed by this approach. Their investigations brought a number of new notions and results in the theory of Sobolev spaces W;(D) which, in turn, enabled us to create a sufficiently complete theory of solvability of elliptical equations. Nowadays the mathematical theory of radiative transfer problems and kinetic equations is an extensive area of modern mathematical physics. It has various applications in astrophysics, the theory of nuclear reactors, geophysics, the theory of chemical processes, semiconductor theory, fluid mechanics, etc. [25,29,31,39,40, 47, 52, 78, 83, 94, 98, 120, 124, 125, 135, 146].

Boundary Value Problems for Transport Equations

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Publisher :
ISBN 13 : 9781461219958
Total Pages : 300 pages
Book Rating : 4.2/5 (199 download)

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Book Synopsis Boundary Value Problems for Transport Equations by : Valeri Agoshkov

Download or read book Boundary Value Problems for Transport Equations written by Valeri Agoshkov and published by . This book was released on 1998-09-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytical Solution Methods for Boundary Value Problems

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Publisher : Academic Press
ISBN 13 : 0128043636
Total Pages : 200 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Analytical Solution Methods for Boundary Value Problems by : A.S. Yakimov

Download or read book Analytical Solution Methods for Boundary Value Problems written by A.S. Yakimov and published by Academic Press. This book was released on 2016-08-13 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content

Transport Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821813201
Total Pages : 340 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Transport Theory by : Richard Bellman

Download or read book Transport Theory written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1969 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The industrial and military applications of atomic energy have stimulated much mathematical research in neutron transport theory. The possibility of controlled thermonuclear processes has similarly focussed attention upon plasmas, sometimes called the "fourth state of matter". Independently, many classical aspects of kinetic theory and radiative transfer theory have been studied both because of their basic mathematical interest and of their physical applications to areas such as upper-atmosphere meteorology - introduction.

Transport Equation and Tomography

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Publisher : VSP
ISBN 13 : 9789067643542
Total Pages : 224 pages
Book Rating : 4.6/5 (435 download)

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Book Synopsis Transport Equation and Tomography by : D. S. Anikonov

Download or read book Transport Equation and Tomography written by D. S. Anikonov and published by VSP. This book was released on 2002 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals mainly with the results of the authors' research devoted to both the study of the transport equation (the linear Boltzmann equation) and its applications in X-ray tomography. The introduction gives an outline of the book and deals with certain aspects of the methodology. The first part of the book is devoted to the investigation of known and new problems for the stationary transport equation of a general form. New problems are treated as problems of tomography. The second part deals with the monoenergetic transport equation. This book will be of interest to specialists in transport theory and tomography.

The Numerical Solution of Ordinary and Partial Differential Equations

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Publisher : World Scientific
ISBN 13 : 9814635111
Total Pages : 348 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell

Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by World Scientific. This book was released on 2014-12-16 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland

Numerical Methods for Chemical Engineering

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Publisher : Cambridge University Press
ISBN 13 : 9780521859714
Total Pages : 496 pages
Book Rating : 4.8/5 (597 download)

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Book Synopsis Numerical Methods for Chemical Engineering by : Kenneth J. Beers

Download or read book Numerical Methods for Chemical Engineering written by Kenneth J. Beers and published by Cambridge University Press. This book was released on 2007 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of numerical mathematics and scientific computing to chemical engineering.

Differential Equations and Boundary Value Problems

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Publisher : Pearson
ISBN 13 : 9780321796981
Total Pages : 0 pages
Book Rating : 4.7/5 (969 download)

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Book Synopsis Differential Equations and Boundary Value Problems by : Charles Henry Edwards

Download or read book Differential Equations and Boundary Value Problems written by Charles Henry Edwards and published by Pearson. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.

Spectral Elements for Transport-Dominated Equations

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Publisher : Springer
ISBN 13 : 9783642591860
Total Pages : 215 pages
Book Rating : 4.5/5 (918 download)

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Book Synopsis Spectral Elements for Transport-Dominated Equations by : Daniele Funaro

Download or read book Spectral Elements for Transport-Dominated Equations written by Daniele Funaro and published by Springer. This book was released on with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential model problems presenting multiscale solutions. This is the case, for instance, with functions displaying a smooth behavior, except in certain regions where sudden and sharp variations are localized. Typical examples are internal or boundary layers. When the number of degrees of freedom in the discretization process is not sufficient to ensure a fine resolution of the layers, some stabilization procedures are needed to avoid unpleasant oscillatory effects, without adding too much artificial viscosity to the scheme. In the field of finite elements, the streamline diffusion method, the Galerkin least-squares method, the bub ble function approach, and other recent similar techniques provide excellent treatments of transport equations of elliptic type with small diffusive terms, referred to in fluid dynamics as advection-diffusion (or convection-diffusion) equations. Goals This book is an attempt to guide the reader in the construction of a computa tional code based on the spectral collocation method, using algebraic polyno mials. The main topic is the approximation of elliptic type boundary-value par tial differential equations in 2-D, with special attention to transport-diffusion equations, where the second-order diffusive terms are strongly dominated by the first-order advective terms. Applications will be considered especially in the case where nonlinear systems of partial differential equations can be re duced to a sequence of transport-diffusion equations.

Transport Theory

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Publisher : CRC Press
ISBN 13 : 1000946541
Total Pages : 479 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Transport Theory by : Paul Nelson

Download or read book Transport Theory written by Paul Nelson and published by CRC Press. This book was released on 2023-05-31 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes seminal papers on technical subjects—transport theory, invariant imbedding, and integral equations—presented as contributions to honour George Milt Wing in celebration of his 65th birth anniversary in 1988.

A Unified Approach to Boundary Value Problems

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Publisher : SIAM
ISBN 13 : 089871706X
Total Pages : 328 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis A Unified Approach to Boundary Value Problems by : Athanassios S. Fokas

Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas and published by SIAM. This book was released on 2008-01-01 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.

Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding

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Publisher : Academic Press
ISBN 13 : 9780080956091
Total Pages : 322 pages
Book Rating : 4.9/5 (56 download)

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Book Synopsis Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding by :

Download or read book Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding written by and published by Academic Press. This book was released on 1973-08-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Numerical Solution of Nonlinear Boundary Value Problems with Applications

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Publisher : Courier Corporation
ISBN 13 : 0486463001
Total Pages : 338 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Numerical Solution of Nonlinear Boundary Value Problems with Applications by : Milan Kubicek

Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

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Publisher : SIAM
ISBN 13 : 9781611971231
Total Pages : 620 pages
Book Rating : 4.9/5 (712 download)

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Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher

Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Nonlinear Ordinary Differential Equations in Transport Processes

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Publisher : Academic Press
ISBN 13 : 0080955509
Total Pages : 282 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Nonlinear Ordinary Differential Equations in Transport Processes by : W. F. Ames

Download or read book Nonlinear Ordinary Differential Equations in Transport Processes written by W. F. Ames and published by Academic Press. This book was released on 1968 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Ordinary Differential Equations in Transport Processes

Boundary Value Problems for Elliptic Systems

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Publisher : Cambridge University Press
ISBN 13 : 0521430119
Total Pages : 659 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Boundary Value Problems for Elliptic Systems by : J. T. Wloka

Download or read book Boundary Value Problems for Elliptic Systems written by J. T. Wloka and published by Cambridge University Press. This book was released on 1995-07-28 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.

Student Solutions Manual, Boundary Value Problems

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Publisher : Academic Press
ISBN 13 : 0123756642
Total Pages : 152 pages
Book Rating : 4.1/5 (237 download)

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Book Synopsis Student Solutions Manual, Boundary Value Problems by : David L. Powers

Download or read book Student Solutions Manual, Boundary Value Problems written by David L. Powers and published by Academic Press. This book was released on 2009-07-13 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Student Solutions Manual, Boundary Value Problems