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ABSTRACT
In this article, we introduce a finite-difference method to solve linear and nonlinear third-order boundary-value problems. We use only four grid points in this method of solution. This method is convergent to fourth-order accuracy. In addition, we show that this method is unconditionally stable. The Falkner-Skan equation and the Blasius equation are considered as special cases of nonlinear problems. Numerical examples are given to illustrate the method and its convergence.
The authors are indebted to Prof. S. E. El-Gendi for various valuable suggestions and constructive criticism.