Numerical solution of general boundary layer problems by the method of di erential quadrature

Accurate numerical solutions to some boundary layer equations are presentedfor boundary layer ows of incompressible newtonian uid over a semi-innite plate. thedierential quadrature method (dqm) is rst used to reduce the governing nonlineardierential equations to a set of nonlinear algebraic equations. the newton-raphsonmethod is then employed to solve the resulting system of nonlinear algebraic equations.the proposed formulation is applied here to solve some boundary layer problems, includingblasius, sakiadis, falkner-skan, magnetohydrodynamic (mhd) falkner-skan, jeery-hamel, unsteady two-dimensional and three-dimensional mhd ows. a simple schemeis also presented for solving the blasius boundary layer equation. in this technique,the blasius boundary value problem is rst converted to a pair of nonlinear initial-valueproblems and then solved by a step-by-step dqm. the accuracy and eciency of theproposed formulations are demonstrated by comparing the calculated results with those ofother numerical and semi-analytical methods. accurate numerical solutions are achievedusing both formulations via a small number of grid points for all the cases considered.