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

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.