Download or read book Quasilinearization and Invariant Imbedding written by E. Stanley Lee and published by Elsevier. This book was released on 2016-06-04 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quasilinearization and Invariant Imbedding written by Eugene Stanley Lee and published by . This book was released on 1968 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasilinearization and Invariant Imbedding written by L. Stanley Lee and published by . This book was released on 1968 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasilinearization Invariant Imbedding and the Calculation of Eigenvalues written by Richard Bellman and published by . This book was released on 1965 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Dynamic programming invariant imbedding quasi linearization written by Richard Bellman and published by . This book was released on 1964 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Imbedding written by R.E. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamic Programming Invariant Imbedding and Quasilinearization Comparisons and Interconnections written by R. E. Bellman and published by . This book was released on 1964 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Water Resources Modeling by Quasilinearization and Invariant Imbedding written by Irving Keao Hwang and published by . This book was released on 1970 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasilinearization and Nonlinear Boundary value Problems written by Richard Bellman and published by New York : American Elsevier. This book was released on 1965 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Methods for Modeling of Nonlinear Systems written by Anatoli Torokhti and published by Academic Press. This book was released on 1974-02-12 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Vistas of Modern Mathematics written by Richard Bellman and published by University Press of Kentucky. This book was released on 2014-07-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid advances in the physical and biological sciences and in related technologies have brought about equally farreaching changes in mathematical research. Focusing on control theory, invariant imbedding, dynamic programming, and quasilinearization, Mr. Bellman explores with ease and clarity the mathematical research problems arising from scientific questions in engineering, physics, biology, and medicine. Special attention is paid in these essays to the use of the digital computer in obtaining the numerical solution of numerical problems, its influence in the formulation of new and old scientific problems in new terms, and to some of the effects of the computer revolution on educational and social systems. The new opportunities for mathematical research presage, Bellman concludes, a renaissance of mathematics in human affairs by involving it closely in the problems of society.
Download or read book Numerical Studies of a Two point Nonlinear Boundary Value Problem Using Dynamic Programming Invariant Imbedding and Quasilinearization written by R. E. Bellman and published by . This book was released on 1964 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories of quasilinearization, dynamic programming and invariant imbedding are applied to the numerical solution of a single variational problem. Their advantages and disadvantages are discussed, and FORTRAN programs and numerical results are included. (Author).
Download or read book Nonlinear Processes in Engineering Mechanics written by Nestor DiStefano and published by . This book was released on 1974 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A New Predictor corrector Method for Quasilinear First order Partial Differential Equations written by J. L. Casti and published by . This book was released on 1968 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: An effective, efficient method is given, exploiting the techniques of invariant imbedding and quasilinearization, for numerically solving quasilinear first-order partial differential equations. It is known that certain nonlinear two-point boundary-value problems can be converted into initial-value problems for a related quasilinear first-order partial differential equation. It is observed, conversely, that the treatment of the partial differential equation can be reduced to solving the two-point boundary-value problem by using quasilinearization. Use of standard finite difference methods to predict, and quasilinearization to correct, can yield precision solutions for the partial differential equation. (Author).
Download or read book The Brachistochronenamic Problem Solved by Invariant Imbedding written by Moo-Zung Lee and published by . This book was released on 1967 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Differential Equations written by Daniel Zwillinger and published by Academic Press. This book was released on 2014-05-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Methods XIB written by Douglas Henderson and published by Elsevier. This book was released on 2012-12-02 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physical Chemistry: An Advanced Treatise, Volume XIB: Mathematical Methods focuses on mathematical techniques that consist of concepts relating to differentiation and integration. This book discusses the methods in lattice statistics, Pfaffian solution of the planar Ising problem, and probability theory and stochastic processes. The random variables and probability distributions, non-equilibrium problems, Brownian motion, and scattering theory are also elaborated. This text likewise covers the elastic scattering from atoms, solution of integral and differential equations, concepts in graph theory, and theory of operator equations. This volume provides graduate and physical chemistry students a basic understanding of mathematical techniques important in chemistry.
