Polynomial and rational approximation of boundary layer problems with the Tau method
Abstract
The paper discusses the application of the recursive formulation of the Tau method to the construction of polynomial and rational approximations to the solution of the boundary layer problem. A linear boundary value problem for a second order differential equation with a significant first derivative, and a model nonlinear singularly perturbed problem with a continuous locus of singular points are used as examples. Numerical solutions are obtained by means of a simple computational procedure. The rational Tau approximations have a high degree of resolution of sharp falls in function values even for approximations of a very low order.
 Publication:

Boundary and Interior Layers  Computational and Asymptotic Methods
 Pub Date:
 1980
 Bibcode:
 1980bilc.proc..387O
 Keywords:

 Approximation;
 Boundary Layer Equations;
 Computational Fluid Dynamics;
 Polynomials;
 Boundary Value Problems;
 Differential Equations;
 Finite Difference Theory;
 Perturbation Theory;
 Fluid Mechanics and Heat Transfer