Iterative operator-splitting methods for Time-irreversible Systems: Theory and Application to Advection-Diffusion Equations

Juergen Geiser , Friedrich Krien

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 14 pp.

MSC 2000

65L05 Initial value problems

65M15 Error bounds

Abstract
In this paper, we deduce higher order error bounds for iterative operator splitting methods for time-irreversible systems of linear advection-diffusion equations. involving time-irreversible diffusion and a reversible advection part. We apply our analysis to bounded our advection operator with the diffusion operator (A-boundedness). We deduce a global error estimates which implies that any time-irreversible time-splitting methods retains its classical convergence of linear advection-diffusion equations, under some assumptions to the exact solution. Numerical results illustrate our theoretical results.