Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unconditionally stable exponential time differencing schemes for the
  mass-conserving Allen-Cahn equation with nonlocal and local effects   It is well known that the classic Allen-Cahn equation satisfies the maximum
bound principle (MBP), that is, the absolute value of its solution is uniformly
bounded for all time by certain constant under suitable initial and boundary
conditions. In this paper, we consider numerical solutions of the modified
Allen-Cahn equation with a Lagrange multiplier of nonlocal and local effects,
which not only shares the same MBP as the original Allen-Cahn equation but also
conserves the mass exactly. We reformulate the model equation with a linear
stabilizing technique, then construct first- and second-order exponential time
differencing schemes for its time integration. We prove the unconditional MBP
preservation and mass conservation of the proposed schemes in the time discrete
sense and derive their error estimates under some regularity assumptions.
Various numerical experiments in two and three dimensions are also conducted to
verify the theoretical results.

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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int