Application of the Method of Invariant Imbedding to the Eigenvalue and Eigenlength Problem for Ordinary Differential Equations PDF Download
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Author: Melvin R. Scott
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 114
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Book Description
Author: Melvin R. Scott
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 114
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Book Description
Author: R. Bellman
Publisher: SIAM
ISBN: 0898713048
Category : Mathematics
Languages : en
Pages : 263
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Book Description
A classic volume describing the foundations of invariant imbedding, re-issued due to a revival of interest in this area.
Author: Melvin R. Scott
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Author: Richard Bellman
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 280
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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: Richard Bellman
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Author: Richard Bellman
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 14
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Book Description
Several eigenvalue problems for systems of ordinary differential equations are considered. They are resolved computationally using the quasilinearization technique, a quadratically convergent successive approximation scheme. The essential idea presented is to consider an eigenvalue problem to be a system identification problem. Also shown is the use of invariant imbedding techniques to obtain good initial estimates for eigenvalues in some neutron multiplication processes. (Author).
Author: Harvard Lomax
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 50
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Book Description
Author: R. Mennicken
Publisher: Elsevier
ISBN: 0080537731
Category : Mathematics
Languages : en
Pages : 519
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Book Description
This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations. In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent to a first order system, the main techniques are developed for systems. Asymptotic fundamental systems are derived for a large class of systems of differential equations. Together with boundary conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10. The contour integral method and estimates of the resolvent are used to prove expansion theorems. For Stone regular problems, not all functions are expandable, and again relatively easy verifiable conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable. Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such as the Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated. Key features: • Expansion Theorems for Ordinary Differential Equations • Discusses Applications to Problems from Physics and Engineering • Thorough Investigation of Asymptotic Fundamental Matrices and Systems • Provides a Comprehensive Treatment • Uses the Contour Integral Method • Represents the Problems as Bounded Operators • Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions
Author: Xerox University Microfilms
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 856
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Book Description
