A New Optimality Property of Strang's Splitting

10/13/2022

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by   Fernando Casas, et al.

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For systems of the form q̇ = M^-1 p, ṗ = -Aq+f(q), common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems q̇ = M^-1 p, ṗ = -Aq and q̇ = 0, ṗ = f(q). We show that the well-known Strang splitting is optimally stable in the sense that, when applied to a relevant model problem, it has a larger stability region than alternative integrators. This generalizes a well-known property of the common Störmer/Verlet/leapfrog algorithm, which of course arises from Strang splitting based on the (kinetic/potential) split systems q̇ = M^-1 p, ṗ = 0 and q̇ = 0, ṗ = -Aq+f(q).