Author: E. Stanley Lee
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
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.
Quasilinearization and Invariant Imbedding
Author: E. Stanley Lee
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
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.
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
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.
Quasilinearization and Invariant Imbedding
Author: Eugene Stanley Lee
Publisher:
ISBN:
Category : Adaptive control systems
Languages : en
Pages : 329
Book Description
Publisher:
ISBN:
Category : Adaptive control systems
Languages : en
Pages : 329
Book Description
Quasilinearization and Invariant Imbedding
Author: L. Stanley Lee
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Quasilinearization, Invariant Imbedding, and the Calculation of Eigenvalues
Author: Richard Bellman
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 14
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).
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 14
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).
Dynamic programming, invariant imbedding, quasi linearization
Author: Richard Bellman
Publisher:
ISBN:
Category :
Languages : en
Pages : 92
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 92
Book Description
Invariant Imbedding
Author: R.E. Bellman
Publisher: Springer Science & Business Media
ISBN: 364246274X
Category : Business & Economics
Languages : en
Pages : 157
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.
Publisher: Springer Science & Business Media
ISBN: 364246274X
Category : Business & Economics
Languages : en
Pages : 157
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.
Dynamic Programming, Invariant Imbedding and Quasilinearization. Comparisons and Interconnections
Author: R. E. Bellman
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 16
Book Description
A nonlinear two-point boundary value problem arising from a variational context is considered from several points of view. First a direct computational solution via quasilinearization is discussed. This method is quadratically convergent. Then the boundary value problem is converted into an initial value problem using dynamic programming and invariant imbedding. Some aspects of combining the methods in a single calculation are discussed. This gives rise to attractive predictor-corrector integration schemes. In addition, an alternative to the usual Hamilton-Jacobi integration theory for the integration of the Euler equation is given. (Author).
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 16
Book Description
A nonlinear two-point boundary value problem arising from a variational context is considered from several points of view. First a direct computational solution via quasilinearization is discussed. This method is quadratically convergent. Then the boundary value problem is converted into an initial value problem using dynamic programming and invariant imbedding. Some aspects of combining the methods in a single calculation are discussed. This gives rise to attractive predictor-corrector integration schemes. In addition, an alternative to the usual Hamilton-Jacobi integration theory for the integration of the Euler equation is given. (Author).
Water Resources Modeling by Quasilinearization and Invariant Imbedding
Author: Irving Keao Hwang
Publisher:
ISBN:
Category :
Languages : en
Pages : 306
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 306
Book Description
Computational Methods for Modeling of Nonlinear Systems
Author: Anatoli Torokhti
Publisher: Academic Press
ISBN: 9780122180507
Category : Mathematics
Languages : en
Pages : 322
Book Description
Publisher: Academic Press
ISBN: 9780122180507
Category : Mathematics
Languages : en
Pages : 322
Book Description
Quasilinearization and Nonlinear Boundary-value Problems
Author: Richard Bellman
Publisher: New York : American Elsevier
ISBN:
Category : Boundary value problems
Languages : en
Pages : 232
Book Description
Publisher: New York : American Elsevier
ISBN:
Category : Boundary value problems
Languages : en
Pages : 232
Book Description