Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Analysis of Approximation Algorithms for Iterated Stochastic
  Integrals and a Julia and MATLAB Simulation Toolbox   For the approximation and simulation of twofold iterated stochastic integrals
and the corresponding L\'{e}vy areas w.r.t. a multi-dimensional Wiener process,
we review four algorithms based on a Fourier series approach. Especially, the
very efficient algorithm due to Wiktorsson and a newly proposed algorithm due
to Mrongowius and R\"ossler are considered. To put recent advances into
context, we analyse the four Fourier-based algorithms in a unified framework to
highlight differences and similarities in their derivation. A comparison of
theoretical properties is complemented by a numerical simulation that reveals
the order of convergence for each algorithm. Further, concrete instructions for
the choice of the optimal algorithm and parameters for the simulation of
solutions for stochastic (partial) differential equations are given.
Additionally, we provide advice for an efficient implementation of the
considered algorithms and incorporated these insights into an open source
toolbox that is freely available for both Julia and MATLAB programming
languages. The performance of this toolbox is analysed by comparing it to some
existing implementations, where we observe a significant speed-up.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga