Integral Equation Formulation and Numerical Solution of Blasius Boundary Layer Problem

The well-known Blasius boundary layer fluid flow problem is a third order nonlinear ordinary differential equation derived from the Navier-Stokes equations. We use a kind of transformation and convert this problem to a nonlinear Volterra integral equation with some properties such that we can apply the quasilinearization technique to this equation which gives two coupled sequences of linear Volterra integral equations. The coupled linear integral equations may be solved by collocation method numerically and this gives an approximation solution for nonlinear integral equation and has this advantage that we do not encounter solving nonlinear algebraic systems. By employing the used transformation numerical solving of the Blasius equation are given. The error of the method has a quadratically convergence in iterative schemes and an error of order O(hm) for collocation method.