Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast second-order evaluation for variable-order Caputo fractional
  derivative with applications to fractional sub-diffusion equations   In this paper, we propose a fast second-order approximation to the
variable-order (VO) Caputo fractional derivative, which is developed based on
$L2$-$1_\sigma$ formula and the exponential-sum-approximation technique. The
fast evaluation method can achieve the second-order accuracy and further reduce
the computational cost and the acting memory for the VO Caputo fractional
derivative. This fast algorithm is applied to construct a relevant fast
temporal second-order and spatial fourth-order scheme ($FL2$-$1_{\sigma}$
scheme) for the multi-dimensional VO time-fractional sub-diffusion equations.
Theoretically, $FL2$-$1_{\sigma}$ scheme is proved to fulfill the similar
properties of the coefficients as those of the well-studied $L2$-$1_\sigma$
scheme. Therefore, $FL2$-$1_{\sigma}$ scheme is strictly proved to be
unconditionally stable and convergent. A sharp decrease in the computational
cost and the acting memory is shown in the numerical examples to demonstrate
the efficiency of the proposed method.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys