  Fourier series multiscale method, a concise and efficient analytical approach
for multiscale computation, will be developed out of this series of papers. In
the fourth paper, the application of the Fourier series multiscale method to
the one- and two-dimensional convection-diffusion-reaction equations is
implemented, where the Fourier series multiscale solutions are derived, the
convergence characteristics of the Fourier series multiscale solutions are
investigated by numerical examples, the schemes for application of the Fourier
series multiscale method are optimized, and the multiscale characteristics of
the convection-diffusion-reaction equations are demonstrated. The preliminary
study on applications verifies the effectiveness of the present Fourier series
multiscale method and provides a reliable reference which can be used for
persistent improvement in computational performance of other multiscale
methods.
