The energy technique for the six-step BDF method

2020/07/17 by Georgios Akrivis, Akrivis, Georgios, Minghua Chen +5 · 3 citations
Mathematics · Engineering · #Differential Equations and Numerical Methods #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2007.08924

Abstract

In combination with the Grenander--Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental 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.

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