Spectral and finite difference solutions of the Burgers equations (Q1088526)

This is a report of the results by the authors who simultaneously attempted to investigate the accuracy of the spectral method applied to problems admitting solutions with rapid variation. As a test problem nonlinear Burgers equation with a very small viscosity is discussed. Spectral methods are found well suited to the calculation of thin inner layers. The accuracy in the sharp region is acceptable under certain conditions whereas standard numerical schemes such as finite differences suffer from numerical dispersion.