@TechReport{ it:2000-024, author = {Saul Abarbanel and Adi Ditkowski and Bertil Gustafsson}, title = {On error bounds of finite difference approximations to partial differential equations - temporal behavior and rate of convergence}, institution = {Department of Information Technology, Uppsala University}, department = {Division of Scientific Computing}, year = {2000}, number = {2000-024}, month = sep, abstract = {This paper considers a family of spatially semi-discrete approximations, including boundary treatments, to hyperbolic and parabolic equations. We derive the dependence of the error-bounds on time as well as on mesh size.} }