The energy technique for the six-step BDF method

07/17/2020

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by   Georgios Akrivis, et al.

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In combination with the Grenander–Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic requirement of the Nevanlinna–Odeh multipliers that the sum of the absolute values of their components is strictly less than 1, makes the energy technique applicable to the stability analysis of BDF methods for parabolic equations with selfadjoint elliptic part. This is particularly useful for the six-step BDF method for which no Nevanlinna–Odeh multiplier exists. We introduce multipliers satisfying the positivity property for the six-step BDF method and establish stability of the method for parabolic equations.