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 splitting is optimal...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
13.10.2022
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| Abstract | 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 $\dot q = 0$, $\dot p =
-Aq+f(q)$. |
|---|---|
| AbstractList | 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 $\dot q = 0$, $\dot p =
-Aq+f(q)$. |
| Author | Casas, Fernando Shaw, Luke Sanz-Serna, Jesús María |
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| BackLink | https://doi.org/10.48550/arXiv.2210.07048$$DView paper in arXiv |
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| Snippet | 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)... |
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| Title | A New Optimality Property of Strang's Splitting |
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