An Introduction to Invariant Imbedding
An Introduction to Invariant Imbedding

Author: R. Bellman

Publisher: SIAM

Published: 1992-01-01

Total Pages: 263

ISBN-13: 0898713048

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A classic volume describing the foundations of invariant imbedding, re-issued due to a revival of interest in this area.

An Introduction to Invariant Imbedding
An Introduction to Invariant Imbedding

Author: R. Bellman

Publisher: SIAM

Published: 1992-01-01

Total Pages: 265

ISBN-13: 9781611971279

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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.

Quasilinearization, Invariant Imbedding, and the Calculation of Eigenvalues
Quasilinearization, Invariant Imbedding, and the Calculation of Eigenvalues

Author: Richard Bellman

Publisher:

Published: 1965

Total Pages: 14

ISBN-13:

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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).

Non-Self-Adjoint Boundary Eigenvalue Problems
Non-Self-Adjoint Boundary Eigenvalue Problems

Author: R. Mennicken

Publisher: Elsevier

Published: 2003-06-26

Total Pages: 519

ISBN-13: 0080537731

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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 equivalentto a first order system, the main techniques are developed for systems. Asymptotic fundamentalsystems are derived for a large class of systems of differential equations. Together with boundaryconditions, 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 verifiableconditions 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 asthe 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