Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fully discrete approximation of the one-dimensional stochastic heat
  equation   A fully discrete approximation of the one-dimensional stochastic heat
equation driven by multiplicative space-time white noise is presented. The
standard finite difference approximation is used in space and a stochastic
exponential method is used for the temporal approximation. Observe that the
proposed exponential scheme does not suffer from any kind of CFL-type step size
restriction. When the drift term and the diffusion coefficient are assumed to
be globally Lipschitz, this explicit time integrator allows for error bounds in
$L^q(\Omega)$, for all $q\geq2$, improving some existing results in the
literature. On top of this, we also prove almost sure convergence of the
numerical scheme. In the case of non-globally Lipschitz coefficients, we
provide sufficient conditions under which the numerical solution converges in
probability to the exact solution. Numerical experiments are presented to
illustrate the theoretical results.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th