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

✍ Scribed by A. Karageorghis; T. N. Phillips; A. R. Davies

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 433 KB
• Volume: 26
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620260404

✦ Synopsis

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.