Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and convergence of Strang splitting. Part I: Scalar Allen-Cahn
  equation   We consider a class of second-order Strang splitting methods for Allen-Cahn
equations with polynomial or logarithmic nonlinearities. For the polynomial
case both the linear and the nonlinear propagators are computed explicitly. We
show that this type of Strang splitting scheme is unconditionally stable
regardless of the time step. Moreover we establish strict energy dissipation
for a judiciously modified energy which coincides with the classical energy up
to $\mathcal O(\tau)$ where $\tau$ is the time step. For the logarithmic
potential case, since the continuous-time nonlinear propagator no longer enjoys
explicit analytic treatments, we employ a second order in time two-stage
implicit Runge--Kutta (RK) nonlinear propagator together with an efficient
Newton iterative solver. We prove a maximum principle which ensures phase
separation and establish energy dissipation law under mild restrictions on the
time step. These appear to be the first rigorous results on the energy
dissipation of Strang-type splitting methods for Allen-Cahn equations.

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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom