Similarity Solutions for Partial Differential Equations Generated by Finite and Infinitesimal Groups,
Abstract
The problem of developing systematic methods for obtaining similarity variables is considered for partial differential equations. Similarity variables are a set of transformations which reduce a partial differential equation to an ordinary differential equation. This paper considers two methods of generating similarity variables. The first method uses a group of finite transformations and the second uses a group of infinitesimal transformations. The mathematical theory for both techniques is described and illustrated. The two methods of obtaining similarity variables are applied to the Burgers' equation u(sub y) + u(u sub x) = u sub xx and to the laminar boundary layer equations with a pressure gradient. In all cases considered, new types of similarity variables are found. In addition, the auxiliary conditions are discussed in the light of the new similarity variables obtained for the boundary layer equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1971
- Accession Number
- AD0733497
Entities
People
- Henry S. Woodard
- William F. Ames
Organizations
- University of Iowa