Rates of Convergence of Approximate Solutions of Parabolic Initial-Boundary Value Problems

摘要

This paper presents error estimates for finite difference approximate solutions of initial-boundary value problems for parabolic partial differential equations. Both whole step methods utilizing matrices of positive type and a locally one dimensional method are considered. Many of these results are obtained by techniques presented in Bramble, Hubbard and Thomee where elliptic partial differential equations were examined.