Numerical solution of the Falkner–Skan equation based on quasilinearization

• Published in: Applied mathematics and computation Vol. 215; no. 7; pp. 2472 - 2485
• Main Authors: Zhu, Shengfeng, Wu, Qingbiao, Cheng, Xiaoliang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2009; Elsevier
• Subjects: Cubic spline; Exact sciences and technology; Falkner–Skan equation; Free boundary value problem; Infinite interval; Mathematical analysis; Mathematics; Nonlinear boundary value problems; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Partial differential equations; Partial differential equations, boundary value problems; Quasilinearization method; Sciences and techniques of general use; Nonlinear boundary value problems; Infinite interval; Falkner–Skan equation; Quasilinearization method; Free boundary value problem; Cubic spline; Free boundary; Numerical linear algebra; Iterative method; Nonlinear problems; Free boundary problem; Algorithm; Partial differential equation; Numerical analysis; Boundary value problem; Linear system; Applied mathematics; Numerical solution; Falkner-Skan equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.08.047

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.