Differential Equations and Group Methods for Scientists and Engineers
| Authors | Hill, James M. |
| Tags | Differential equations -- Numerical solutions, Transformation groups, Differentialgleichung, Numerisches Verfahren, Transformationsgruppe, Lie theory |
| Publisher | CRC Press |
| Published | 12 gen 1992 |
| Date | 12 dic 2019 |
| Languages | eng |
| Identifiers | isbn: 9780849344428, oclc: 25317377 |
| Formats | DJVU |
Description
Presents a basic introduction to the technically complex area of invariant one-parameter Lie group methods and their use in solving differential equations. This book features discussions on ordinary differential equations (first, second, and higher order) in addition to partial differential equations (linear and nonlinear).
cited in
- M. C. Nucci, “The Complete Kepler Group Can Be Derived by Lie Group Analysis,” Journal of Mathematical Physics 37, no. 4 (April 1, 1996): 1772–75.
This book is a republication of the author's earlier book [Solution of differential equations by means of one-parameter groups, Pitman, Boston, 1982; MR0665427]. The book does a nice job of presenting the basic mechanics of Lie's symmetry theory for differential equations and contains many examples worked out in detail. Unfortunately, the summary of research areas given at the end of the book does not accurately reflect the many recent developments in the subject. See, for example, work of G. W. Bluman and S. Kumei [Symmetries and differential equations, Springer, New York, 1989; MR1006433] and P. J. Olver [Applications of Lie groups to differential equations, second edition, Springer, New York, 1993]. Reviewed by Ian M. Anderson