Fourth-order finite-difference method for third-order boundary-value problems

摘要

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.