Similarity Methods for Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Similarity Methods for Differential Equations PDF full book. Access full book title Similarity Methods for Differential Equations by G.W. Bluman. Download full books in PDF and EPUB format.
Author: G.W. Bluman
Publisher: Springer Science & Business Media
ISBN: 1461263948
Category : Mathematics
Languages : en
Pages : 343
Get Book
Book Description
The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation.
Author: G.W. Bluman
Publisher: Springer Science & Business Media
ISBN: 1461263948
Category : Mathematics
Languages : en
Pages : 343
Get Book
Book Description
The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel's approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential equation the knowledge of a group leads immediately to quadrature, and for a higher order equation (or system) to a reduction in order. In another sense this theory is somewhat disappointing in that for a first-order differ ential equation essentially no systematic way can be given for finding the groups or showing that they do not exist for a first-order differential equation.
Author: George W. Bluman
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 332
Get Book
Book Description
Author: Lawrence Dresner
Publisher: Pitman Advanced Publishing Program
ISBN:
Category : Mathematics
Languages : en
Pages : 148
Get Book
Book Description
Author: Douglas Eugene Abbott
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 58
Get Book
Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book
Book Description
A code has been written to use the algebraic computer system MACSYMA to generate systematically the infinitesimal similarity groups corresponding to systems of quasi-linear partial differential equations. The infinitesimal similarity groups can be used to find exact solutions of the partial differential equations. In an example from fluid mechanics the similarity method using the computer code reproduces immediately a solution obtained from dimensional analysis.
Author: P.L. Sachdev
Publisher: CRC Press
ISBN: 1000611418
Category : Mathematics
Languages : en
Pages : 172
Get Book
Book Description
Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents
Author: Bahman Zohuri
Publisher: Springer
ISBN: 3319134760
Category : Technology & Engineering
Languages : en
Pages : 372
Get Book
Book Description
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
Author: J L Schwarzmeier
Publisher: Legare Street Press
ISBN: 9781019942116
Category :
Languages : en
Pages : 0
Get Book
Book Description
This book provides an introduction to similarity solutions with a focus on systems of partial differential equations. Using the powerful software package MACSYMA, the authors demonstrate how to find exact solutions and approximate solutions using perturbation methods. A must-read for anyone interested in partial differential equations and numerical methods. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Bahman Zohuri
Publisher:
ISBN: 9783319134772
Category :
Languages : en
Pages :
Get Book
Book Description
· Provides innovative techniques for solving complex nonlinear partial differential equations, previously only available to scientists involved in classified government funded projects. · Goes beyond the traditional Pi (Buckingham) Theorem method to apply dimensional analysis to gas dynamics and thermal hydraulics problems where both laminar and turbulent fluids come into play · Includes specific examples demonstrating how dimensional analysis can shed light on applications from shock wave impact prediction to plasma confinement. · Presents a unique approach to similarity methods by discussing Chaos, Fractals and Arcadia, in addition to the more common Self-Similarity and Fractals Techniques This ground-breaking reference provides an overview of key concepts in dimensional analysis and the scientific approach of similarity methods, including a uniquely robust discussion on self-similarity solutions of the First and Second kinds. The coverage pushes well beyond traditional applications in fluid mechanics and gas dynamics to demonstrate how powerful self-similarity can be in solving complex problems across many diverse fields, using nonlinear Partial Differential Equations (PDEs) by reducing them to Ordinary Differential Equations (ODEs) with a simple traditional analytical solution approach. Of particular interest is the book's coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering from Heat Transfer and Thermal Hydraulic points of view. Numerous practical examples of dimensional analysis problems are presented throughout each chapter, with additional problems presented in each appendix, allowing readers to link the book's theoretical explanations and step-by-step mathematical solutions to practical implementations.
Author: L. I. Sedov
Publisher: CRC Press
ISBN: 1351416561
Category : Science
Languages : en
Pages : 230
Get Book
Book Description
Similiarity and Dimensional Methods in Mechanics, 10th Edition is an English language translation of this classic volume examining the general theory of dimensions of physical quantities, the theory of mechanical and physical similarity, and the theory of modeling. Several examples illustrate the use of the theories of similarity and dimensions for establishing fundamental mechanical regularities in aviation, explosions, and astrophysics, as well as in the hydrodynamics of ships. Other interesting areas covered include the general theory of automodel motions of continuum media, the theory of propagation of explosion waves in gases, the theory of one-dimensional nonestablished motion in gases, the fundamentals of the gas-dynamics theory of atom-bomb explosion in the atmosphere and the theory of averaging of gaseous flows in channels. Aspects of modeling include the dimensionless characteristics of compressor operation, the theories of engine thrust, and efficiency of an ideal propeller for subsonic and supersonic speeds. Similiarity and Dimensional Methods in Mechanics, 10th Edition is an ideal volume for researchers and students involved in physics and mechanics.
