Numerical solution of boundary-layer problems

A spectral method of solving boundary-layer problems is presented. The method uses Laguerre polynomials to construct orthogonal basis functions that satisfy far-field conditions automatically. An implementation of the method is outlined and two illustrative examples are presented. Both examples have known solutions, which are used to test the accuracy and computational efficiency of the method. Useful estimates of the numerical error are obtained and a strategy is developed to adjust the basis functions in order to optimize the rate of convergence.