Initial Value Methods For Boundary Value Problems Theory And Application Of Invariant Imbedding
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Initial Value Methods For Boundary Value Problems Theory And Application Of Invariant Imbedding
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Author :
language : en
Publisher: Academic Press
Release Date : 1973-08-15
Initial Value Methods For Boundary Value Problems Theory And Application Of Invariant Imbedding written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-08-15 with Mathematics categories.
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
An Introduction To Invariant Imbedding
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Author : R. Bellman
language : en
Publisher: SIAM
Release Date : 1992-01-01
An Introduction To Invariant Imbedding written by R. Bellman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
A classic volume describing the foundations of invariant imbedding, re-issued due to a revival of interest in this area.
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations
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Author : A.K. Aziz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations written by A.K. Aziz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Factorization Of Boundary Value Problems Using The Invariant Embedding Method
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Author : Jacques Henry
language : en
Publisher: Elsevier
Release Date : 2016-11-09
Factorization Of Boundary Value Problems Using The Invariant Embedding Method written by Jacques Henry and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-09 with Mathematics categories.
Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems. Develops the invariant embedding technique for boundary value problems Makes a link between control theory, boundary value problems and the Gauss factorization Presents a new theory for successively solving linear elliptic boundary value problems Includes a transformation in two initial value problems that are uncoupled
An Introduction To Invariant Imbedding
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Author : Richard Bellman
language : en
Publisher: Wiley-Interscience
Release Date : 1975
An Introduction To Invariant Imbedding written by Richard Bellman and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Derivation And Validation Of An Initial Value Method For Certain Nonlinear Two Point Boundary Value Problems
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Author : H. H. Kagiwada
language : en
Publisher:
Release Date : 1968
Derivation And Validation Of An Initial Value Method For Certain Nonlinear Two Point Boundary Value Problems written by H. H. Kagiwada and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Much of the theory of invariant imbedding is devoted to the conversion of boundary-value problems into initial-value (Cauchy) problems because of the computational advantages offered by the initial-value formulation. This study describes a technique for transforming a nonlinear two-point boundary-value problem into an initial-value problem and shows, conversely, that the solution of the Cauchy problem does satisfy the original boundary-value problem. The technique given is broad enough to cover many of the equations of radiative transfer, dilute gas dynamics, and optimal control. (Author).
Invariant Imbedding
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Author : R.E. Bellman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Invariant Imbedding written by R.E. Bellman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
Imbedding is a powerful and versatile tool for problem solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.
Handbook Of Differential Equations
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Author : Daniel Zwillinger
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Handbook Of Differential Equations written by Daniel Zwillinger and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Handbook of Differential Equations is a handy reference to many popular techniques for solving and approximating differential equations, including exact analytical methods, approximate analytical methods, and numerical methods. Topics covered range from transformations and constant coefficient linear equations to finite and infinite intervals, along with conformal mappings and the perturbation method. Comprised of 180 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.
Computational Methods In Engineering Boundary Value Problems
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Author : T.Y. Na
language : en
Publisher: Academic Press
Release Date : 1980-01-18
Computational Methods In Engineering Boundary Value Problems written by T.Y. Na and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-18 with Computers categories.
Computational Methods in Engineering Boundary Value Problems
Wave Propagation
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Author : N.D. Bellman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wave Propagation written by N.D. Bellman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The SCQlldIII of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with . physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They· draw upon widely different sections of mathematics.