Time‐accurate solution of advection–diffusion problems by wavelet‐Taylor–Galerkin method
Mani Mehra, B. V. Rathish Kumar · Communications in Numerical Methods in Engineering · 2005
Abstract In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time‐dependent advection–diffusion problems. The discretization in time is performed before the spatial discretization by introducing second‐ and 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 efficiency of our approach. Copyright © 2005 John Wiley & Sons, Ltd.