In this chapter we consider various approaches to construct finite difference schemes with improved convergence order for a singularly perturbed parabolic convection-diffusion equation with sufficiently smooth and piecewise-smooth initial data. There are well elaborated methods: (a) the defect correction, (b) the Richardson extrapolation,

and newly created and developing methods: (c) based on asymptotic constructs, and (d) the additive splitting of singularities.