On high-order compact difference schemes

Abstract

We describe fourth-order difference approximations of two-and three-dimensional boundary value problems for convection-diffusion equations with variable coefficients. We study difference schemes for the Poisson equation in cylindrical coordinates and the conditions for monotonicity and symmetry of the algebraic Systems obtained. We generalize the results to nonstationary problems described by equations of parabolic and hyperbolic types. We formulate and prove theorems on error estimates of approximate Solutions in the uniform norm. ai =°5 -ß$ -07 -flg ~f c = l 'Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia The work was supported by RFBR (99-01-00579) and RFBR-INTAS (95-98).