A New Optimality Property of Strang's Splitting

For systems of the form \(\dot q = M^{-1} p\), \(\dot p = -Aq+f(q)\), common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems \(\dot q = M^{-1} p\), \(\dot p = -Aq\) and \(\dot q = 0\), \(\dot p = f(q)\). We show that the well-known Strang splittin...

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Bibliographic Details
Published inarXiv.org
Main Authors Casas, Fernando, Sanz-Serna, Jesús María, Shaw, Luke
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.02.2023
Subjects
Algorithms
Integrators
Nonlinear systems
Optimization
Splitting
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Summary:For systems of the form \(\dot q = M^{-1} p\), \(\dot p = -Aq+f(q)\), common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems \(\dot q = M^{-1} p\), \(\dot p = -Aq\) and \(\dot q = 0\), \(\dot p = f(q)\). 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 St\"{o}rmer/Verlet/leapfrog algorithm, which of course arises from Strang splitting based on the (kinetic/potential) split systems \(\dot q = M^{-1} p\), \(\dot p = 0\) and \(\dot q = 0\), \(\dot p = -Aq+f(q)\).
ISSN:2331-8422