Spectral collocation methods for the primary two‐point boundary value problem in modelling viscoelastic flows

Abstract

Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two‐point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non‐linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non‐linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non‐linearity. The use of Newton's method to solve the mixed linear‐non‐linear system for the Chebyshev coefficients is successful for highly non‐linear problems without the need for parameter continuation. Copyright © 1988 John Wiley & Sons, Ltd