The Pseudo-wavelet Scheme For Convection Equation

In this paper, we firstly introduce some basic properties of wavelet, which are involved in chapter one .secondly, we introduce orthogonal wavelet bases, scale function and scale equations etc.,which are involver in chapter two .Mainly, we deriver time-accurate wavelet-based schemes for convection equation ,furthermore, we use it for numerical solution of convection equation and make a comparison with exact solution and solution derived from WGM.The validation of WTGM is presented by convection equation. Because of Taylor series expansions of time derivatives,time-accurate is depended on the orders ofΔt ,the higher the order ofΔt is, the higher time-accurate is.WTGM takes advantage of the compression of both the function field and the operator involved, with which the matrix derived by operator is not much dense. Finally, we give another application of WTGM.WTGM have been used in the numerical simulation of merging three vortices, because the problem has the strongest nonlinear interaction.