A new class of implicit–explicit BDF[formula omitted] SAV schemes for general dissipative systems and their error analysis

Abstract

We construct a new class of efficient implicit–explicit (IMEX) BDFk schemes combined with a scalar auxiliary variable (SAV) approach for general dissipative systems. We show that these schemes are unconditionally stable, and lead to a uniform bound of the numerical solution in the norm based on the principal linear operator in the free energy. Based on this uniform bound, we carry out a rigorous error analysis for the kth-order (k=1,2,3,4,5) SAV schemes in a unified form for a class of general dissipative systems. We also present numerical results confirming our theoretical convergence rates.