Calculation of similarity solutions of partial differential equations
When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- DOE Contract Number:
- W-7405-ENG-26
- OSTI ID:
- 5157583
- Report Number(s):
- ORNL/TM-7407
- Country of Publication:
- United States
- Language:
- English
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