Exact And Truncated Difference Schemes For Boundary Value Odes

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Exact and Truncated Difference Schemes for Boundary Value ODEs

Ivan Gavrilyuk,Martin Hermann,Volodymyr Makarov,Myroslav V. Kutniv
Exact and Truncated Difference Schemes for Boundary Value ODEs Book PDF

Author : Ivan Gavrilyuk,Martin Hermann,Volodymyr Makarov,Myroslav V. Kutniv
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 41,6 Mb
Release : 2011-08-12
Category : Mathematics
ISBN : 9783034801072

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Exact and Truncated Difference Schemes for Boundary Value ODEs by Ivan Gavrilyuk,Martin Hermann,Volodymyr Makarov,Myroslav V. Kutniv Pdf

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems. The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

Exact Finite-Difference Schemes

Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov
Exact Finite Difference Schemes Book PDF

Author : Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 246 pages
File Size : 53,5 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783110491326

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Exact Finite-Difference Schemes by Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov Pdf

Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography

Exact Finite-Difference Schemes

Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov
Exact Finite Difference Schemes Book PDF

Author : Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 246 pages
File Size : 48,5 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9783110489729

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Exact Finite-Difference Schemes by Sergey Lemeshevsky,Piotr Matus,Dmitriy Poliakov Pdf

Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography

Mathematical Reviews

Anonim
Mathematical Reviews Book PDF

Author : Anonim
Publisher : Unknown
Page : 836 pages
File Size : 44,8 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015062317204

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Mathematical Reviews by Anonim Pdf

Numerical Solution of Two Point Boundary Value Problems

Herbert B. Keller
Numerical Solution of Two Point Boundary Value Problems Book PDF

Author : Herbert B. Keller
Publisher : SIAM
Page : 69 pages
File Size : 42,5 Mb
Release : 1976-01-01
Category : Mathematics
ISBN : 161197044X

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Numerical Solution of Two Point Boundary Value Problems by Herbert B. Keller Pdf

Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.

Difference Methods for Initial-Boundary-Value Problems and Flow Around Bodies

You-lan Zhu,Xi-chang Zhong,Bing-mu Chen,Zuo-min Zhang
Difference Methods for Initial Boundary Value Problems and Flow Around Bodies Book PDF

Author : You-lan Zhu,Xi-chang Zhong,Bing-mu Chen,Zuo-min Zhang
Publisher : Springer Science & Business Media
Page : 606 pages
File Size : 40,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662067079

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Difference Methods for Initial-Boundary-Value Problems and Flow Around Bodies by You-lan Zhu,Xi-chang Zhong,Bing-mu Chen,Zuo-min Zhang Pdf

Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.

Reviews in Numerical Analysis, 1980-86

Anonim
Reviews in Numerical Analysis 1980 86 Book PDF

Author : Anonim
Publisher : Unknown
Page : 648 pages
File Size : 43,7 Mb
Release : 1987
Category : Numerical analysis
ISBN : UOM:39015016353305

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Reviews in Numerical Analysis, 1980-86 by Anonim Pdf

These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.

Applied Mechanics Reviews

Anonim
Applied Mechanics Reviews Book PDF

Author : Anonim
Publisher : Unknown
Page : 628 pages
File Size : 50,5 Mb
Release : 1974
Category : Mechanics, Applied
ISBN : UCAL:C2682445

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Applied Mechanics Reviews by Anonim Pdf

Hamilton-Jacobi-Bellman Equations

Dante Kalise,Karl Kunisch,Zhiping Rao
Hamilton Jacobi Bellman Equations Book PDF

Author : Dante Kalise,Karl Kunisch,Zhiping Rao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 261 pages
File Size : 53,5 Mb
Release : 2018-08-06
Category : Mathematics
ISBN : 9783110542714

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Hamilton-Jacobi-Bellman Equations by Dante Kalise,Karl Kunisch,Zhiping Rao Pdf

Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme

Numerical Partial Differential Equations

J.W. Thomas
Numerical Partial Differential Equations Book PDF

Author : J.W. Thomas
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 43,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461205692

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Numerical Partial Differential Equations by J.W. Thomas Pdf

Continuing the theme of the first, this second volume continues the study of the uses and techniques of numerical experimentation in the solution of PDEs. It includes topics such as initial-boundary-value problems, a complete survey of theory and numerical methods for conservation laws, and numerical schemes for elliptic PDEs. The author stresses the use of technology and graphics throughout for both illustration and analysis.