A time-accurate pseudo-wavelet scheme for parabolic and hyperbolic PDE's

Abstract

In this paper, we propose wavelet Taylor–Galerkin schemes for parabolic and hyperbolic PDEs taking full advantage of the compression properties of wavelet basis. The discretization in time is performed before the spatial discretization by introducing high-order generalization of the standard time-stepping schemes with the help of Taylor series expansion in time step. Then, we present numerical results for a convection problem in one dimension and Gaussian translating hill problem in two dimensions. Finally, results for the two-dimensional turbulence are shown.