A framework proves that IMEX-LMMs for gradient flows dissipate a modified energy iff the method's generating polynomials are positive on [-1,1], yielding BDF methods up to order 5, a new order-6 method, and a sixth-order barrier for the simple multiplier.
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Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier
A framework proves that IMEX-LMMs for gradient flows dissipate a modified energy iff the method's generating polynomials are positive on [-1,1], yielding BDF methods up to order 5, a new order-6 method, and a sixth-order barrier for the simple multiplier.