A New Optimality Property of Strang's Splitting

2022/10/13 by Casas, Fernando, Sanz-Serna, Jesús María, Shaw, Luke
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2210.07048

Abstract

For systems of the form q = M^-1 p, p = -Aq+f(q), common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems q = M^-1 p, p = -Aq and q = 0, p = 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 q = M^-1 p, p = 0 and q = 0, p = -Aq+f(q).

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