Abstract
We present two iterative methods for solving the Falkner-Skan equation based on the quasilinearization method. We formulate the original problem as a new free boundary value problem. The truncated boundary depending on a small parameter is an unknown free boundary and has to be determined as part of solution. Using a change of variables, the free boundary value problem is transformed to a problem defined on [0, 1]. We apply the quasilinearization method to solve the resulting nonlinear problem. Then we propose two different iterative algorithms by means of a cubic spline solver. Numerical results for various instances are compared with those reported previously in the literature. The comparisons show the accuracy, robustness and efficiency of the presented methodology.
| Original language | English |
|---|---|
| Pages (from-to) | 2472-2485 |
| Number of pages | 14 |
| Journal | Applied Mathematics and Computation |
| Volume | 215 |
| Issue number | 7 |
| DOIs | |
| State | Published - 1 Dec 2009 |
| Externally published | Yes |
Keywords
- Cubic spline
- Falkner-Skan equation
- Free boundary value problem
- Infinite interval
- Nonlinear boundary value problems
- Quasilinearization method
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