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Abstract
We present an extended one-step method of order 5 for the solution of the third-order, nonlinear free boundary-value problem. The Falkner-Skan equation as well as the Blasius equation are special cases of this problem. We prove that this method is A- and L-stable. The method uses a coordinate transformation to map a semi-infinite physical domain to the open unit interval (0, 1). Comparisons are made between the numerical solutions obtained by the proposed method and those obtained by previous authors.
The author is indebted to Prof. S. E. El-Gendi and Prof. I. A. Hassanien for various valuable suggestions and constructive criticism. We express our gratitude to the (unknown) referees for their comments and suggestions.