Invariant Imbedding and Its Applications to Ordinary Differential Equations PDF Download
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Author: Melvin R. Scott
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Author: Melvin R. Scott
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Author: R. Bellman
Publisher: SIAM
ISBN: 9781611971279
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation. The reprinting of this classic volume was prompted by a revival of interest in the subject area because of its uses for inverse problems. The major part of the book consists of applications of the invariant imbedding method to specific areas that are of interest to engineers, physicists, applied mathematicians, and numerical analysts. A large set of problems can be found at the end of each chapter. Numerous problems on apparently disparate matters such as Riccati equations, continued fractions, functional equations, and Laplace transforms are included. The exercises present the reader with "real-life" situations. The material is accessible to a general audience, however, the authors do not hesitate to state, and even to prove, a rigorous theorem when one is available. To keep the original flavor of the book, very few changes were made to the manuscript; typographical errors were corrected and slight changes in word order were made to reduce ambiguities.
Author: R.E. Bellman
Publisher: Springer Science & Business Media
ISBN: 364246274X
Category : Business & Economics
Languages : en
Pages : 157
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Book Description
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.
Author: E. Stanley Lee
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Mathematics in Science and Engineering, Volume 41: Quasilinearization and Invariant Imbedding presents a study on the use of two concepts for obtaining numerical solutions of boundary-value problems—quasilinearization and invariant imbedding. This book emphasizes that the invariant imbedding approach reformulates the original boundary-value problem into an initial value problem by introducing new variables or parameters, while the quasilinearization technique represents an iterative approach combined with linear approximations. This volume focuses on analytical aspects that are concerned with actual convergence rates and computational requirements, considering various efficient algorithms that are suited for various types of boundary-value problems. This publication is a good reference for chemical and control engineers and scientists interested in obtaining numerical solutions of boundary-value problems in their particular fields.
Author: George Milton Wing
Publisher:
ISBN:
Category : Invariant imbedding
Languages : en
Pages : 112
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Book Description
Author:
Publisher: Academic Press
ISBN: 0080956092
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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; andmethods 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 particularbranches, 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
Author: Melvin R. Scott
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 114
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Book Description
Author: James P. Corones
Publisher: SIAM
ISBN: 9780898713053
Category : Science
Languages : en
Pages : 276
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Book Description
This volume on invariant imbedding and inverse problems is based on a conference held in Alberquerque, New Mexico, in April 1990.
Author: Paul Nelson
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
Invariant imbedding is a method for the computational solution of two-point boundary-value problems. One common source of such problems is in the application of the method of lines, or an expansion procedure, to a system of partial differential equations. Such partial differential equations might describe, for example, the dynamic mechanics of structures such as an aircraft fuselage or a missile silo. The research conducted under this grant has been directed toward two objectives. The first objective was to improve the effectiveness and efficiency of invariant imbedding by providing means for automatically controlling the associated computational effort. The second objective was to extend the range of applicability of invariant imbedding to include singular two-point boundary-value problems. Such singular problems arise, for example, by applying the method of lines to partial differential equations in spherical or cylindrical coordinate systems. In regard to the first of these objectives, a number of different methods, which are generically termed 'relative-error monitors', have been developed and are in the process of being subjected to computational experimentation. As regards the second objective, it has been shown how to apply the method of invariant imbedding to 'homogeneous' linear two-point boundary-value problems. The further extension to inhomogeneous problems is presently being pursued. (Author).
Author: Lee
Publisher: Academic Press
ISBN: 0080955495
Category : Computers
Languages : en
Pages : 351
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Book Description
Quasilinearization and invariant imbedding, with applications to chemical engineering and adaptive control
