High-order methods and numerical boundary conditions

Abstract

In this paper we present high-order difference schemes for convection diffusion problems. When we apply high-order numerical methods to problems where physical boundary conditions are not periodic there is a need to choose adequate numerical boundary conditions in order to preserve the high-order accuracy. Next to the boundary we do not usually have enough discrete points to apply the high-order scheme and therefore at these nodes we must consider different approximations, named the numerical boundary conditions.