Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partially Explicit Time Discretization for Nonlinear Time Fractional
  Diffusion Equations   Nonlinear time fractional partial differential equations are widely used in
modeling and simulations. In many applications, there are high contrast changes
in media properties. For solving these problems, one often uses coarse spatial
grid for spatial resolution. For temporal discretization, implicit methods are
often used. For implicit methods, though the time step can be relatively large,
the equations are difficult to compute due to the nonlinearity and the fact
that one deals with large-scale systems. On the other hand, the discrete system
in explicit methods are easier to compute but it requires small time steps. In
this work, we propose the partially explicit scheme following earlier works on
developing partially explicit methods for nonlinear diffusion equations. In
this scheme, the diffusion term is treated partially explicitly and the
reaction term is treated fully explicitly. With the appropriate construction of
spaces and stability analysis, we find that the required time step in our
proposed scheme scales as the coarse mesh size, which creates a great saving in
computing. The main novelty of this work is the extension of our earlier works
for diffusion equations to time fractional diffusion equations. For the case of
fractional diffusion equations, the constraints on time steps are more severe
and the proposed methods alleviate this since the time step in partially
explicit method scales as the coarse mesh size. We present stability results.
Numerical results are presented where we compare our proposed partially
explicit methods with a fully implicit approach. We show that our proposed
approach provides similar results, while treating many degrees of freedom in
nonlinear terms explicitly.

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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat