Numerical solution of the Falkner-Skan equation based on quasilinearization

作者：Zhu Shengfeng^*; Wu Qingbiao; Cheng Xiaoliang

来源：Applied Mathematics and Computation, 2009, 215(7): 2472-2485.

DOI：10.1016/j.amc.2009.08.047

• Falkner-Skan equation
• Nonlinear boundary value problems
• Free boundary value problem
• Quasilinearization method
• Cubic spline
• Infinite interval

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.

• 出版日期2009-12-1
• 单位浙江大学