Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A second-order difference scheme for the time fractional substantial
  diffusion equation   In this work, a second-order approximation of the fractional substantial
derivative is presented by considering a modified shifted substantial
Gr\"{u}nwald formula and its asymptotic expansion. Moreover, the proposed
approximation is applied to a fractional diffusion equation with fractional
substantial derivative in time. With the use of the fourth-order compact scheme
in space, we give a fully discrete Gr\"{u}nwald-Letnikov-formula-based compact
difference scheme and prove its stability and convergence by the energy method
under smooth assumptions. In addition, the problem with nonsmooth solution is
also discussed, and an improved algorithm is proposed to deal with the
singularity of the fractional substantial derivative. Numerical examples show
the reliability and efficiency of the scheme.

5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th