Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence analysis of the time-stepping numerical methods for
  time-fractional nonlinear subdiffusion equations   In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall
inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen
as a generalization of the classical discrete Gr\"{o}nwall inequality. However,
this generalized discrete Gr\"{o}nwall inequality has not been widely applied
in the numerical analysis of the time-stepping methods for the time-fractional
evolution equations. The main purpose of this paper is to show how to apply the
generalized discrete Gr\"{o}nwall inequality to prove the convergence of a
class of time-stepping numerical methods for time-fractional nonlinear
subdiffusion equations, including the popular fractional backward difference
type methods of order one and two, and the second-order fractional
Crank-Nicolson type methods. We obtain the optimal $L^2$ error estimate in
space discretization. The convergence of the fast time-stepping numerical
methods is also proved in a simple manner.

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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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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: comp-gas
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The categories of this paper are: plasm-ph