Similarity Methods for Differential Equations
Title | Similarity Methods for Differential Equations PDF eBook |
Author | G.W. Bluman |
Publisher | Springer Science & Business Media |
Pages | 343 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461263948 |
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.
Similarity Methods for Differential Equations
Title | Similarity Methods for Differential Equations PDF eBook |
Author | George W. Bluman |
Publisher | |
Pages | 332 |
Release | 1975 |
Genre | Differential equations |
ISBN |
G. W. Bluman [and] J. D. Cole ; Similarity Methods for Differential Equations
Title | G. W. Bluman [and] J. D. Cole ; Similarity Methods for Differential Equations PDF eBook |
Author | G. W. Bluman |
Publisher | |
Pages | |
Release | 1974 |
Genre | |
ISBN |
Simple Methods for Classification and Construction of Similarity Solutions of Partial Differential Equations
Title | Simple Methods for Classification and Construction of Similarity Solutions of Partial Differential Equations PDF eBook |
Author | Douglas Eugene Abbott |
Publisher | |
Pages | 58 |
Release | 1960 |
Genre | Boundary value problems |
ISBN |
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists
Title | Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists PDF eBook |
Author | Bahman Zohuri |
Publisher | Springer |
Pages | 379 |
Release | 2015-04-15 |
Genre | Technology & Engineering |
ISBN | 3319134760 |
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.
Similarity Solutions of Systems of Partial Differential Equations Using MACSYMA.
Title | Similarity Solutions of Systems of Partial Differential Equations Using MACSYMA. PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 1979 |
Genre | |
ISBN |
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.
Similarity Method for Differential Equations
Title | Similarity Method for Differential Equations PDF eBook |
Author | Boon-chang Tan |
Publisher | |
Pages | 134 |
Release | 1989 |
Genre | Differential equations |
ISBN |