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

Abstract

The essential character of the primary elliptic‐hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non‐linear fifth‐order two‐point boundary value problem in one dimension. 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 Galerkin formulation. An investigation of the performance of the methods with respect to the level of non‐linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non‐linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non‐linearity. Copyright © 1988 John Wiley & Sons, Ltd