Implicit-explicit BDF k SAV schemes for general dissipative systems and their error analysis
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We construct efficient implicit-explicit BDFk scalar auxiliary variable (SAV) schemes 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 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 typical Allen-Cahn type and Cahn-Hilliard type equations. We also present numerical results confirming our theoretical convergence rates.
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