Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational efficiency of fractional diffusion using adaptive time
  step memory   Numerical solutions to fractional differential equations can be extremely
computationally intensive due to the effect of non-local derivatives in which
all previous time points contribute to the current iteration. In finite
difference methods this has been approximated using the 'short memory effect'
where it is assumed that previous events prior to some certain time point are
insignificant and thus not calculated. Here we present an adaptive time method
for smooth functions that is computationally efficient and results in smaller
errors during numerical simulations. Sampled points along the system's history
at progressively longer intervals are assumed to reflect the values of
neighboring time points. By including progressively fewer points as a function
of time, a temporally 'weighted' history is computed that includes
contributions from the entire past of the system, resulting in increased
accuracy, but with fewer points actually calculated, which ensures
computational efficiency.

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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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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: gr-qc