ERROR ESTIMATES FOR TIME ACCURATE WAVELET BASED SCHEMES FOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

In this study, we derive error estimates for time accurate wavelet based schemes in two stages. First we look at the semi-discrete boundary value problem as a Cauchy problem and use spectral decomposition of self adjoint operators to arrive at the temporal error estimates both in L2 and energy norms. Later, following the wavelet approximation theory, we propose spatial error estimates in L2 and energy norms. And finally arrive at a priori estimates for the fully discrete problem.