Time-accurate solution of advection–di usion problems by wavelet-Taylor–Galerkin method

In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–di usion problems. The discretization in time is performed before the spatial discretization by introducing secondand third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in time step. Numerical schemes taking advantage of the wavelet bases capabilities to compress both functions and operators are presented. Numerical examples demonstrate the e ciency of our approach. Copyright ? 2005 John Wiley & Sons, Ltd.