Maximum time step for the BDF3 scheme applied to gradient flows


For backward differentiation formulae (BDF) applied to gradient flows of semiconvex functions, quadratic stability implies the existence of a Lyapunov functional. We compute the maximum time step which can be derived from quadratic stability for the 3-step BDF method (BDF3). Applications to the asymptotic behaviour of sequences generated by the BDF3 scheme are given.

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The author is thankful to Frédéric Bosio, Anass Bouchriti and Nour Eddine Alaa for helpful discussions. The author also wishes to thank the anonymous referee for his valuable comments.

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Correspondence to Morgan Pierre.

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Pierre, M. Maximum time step for the BDF3 scheme applied to gradient flows. Calcolo 58, 3 (2021).

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  • Gradient system
  • BDF method
  • Semiconvex function
  • Kurdyka–Łojasiewicz property
  • Multivalued dynamical system

Mathematics Subject Classification

  • 65P40
  • 65L04