Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite element methods based on two families of second-order numerical
  formulas for the fractional Cable model with smooth solutions   We apply two families of novel fractional $\theta$-methods, the FBT-$\theta$
and FBN-$\theta$ methods developed by the authors in previous work, to the
fractional Cable model, in which the time direction is approximated by the
fractional $\theta$-methods, and the space direction is approximated by the
finite element method. Some positivity properties of the coefficients for both
of these methods are derived, which are crucial for the proof of the stability
estimates. We analyse the stability of the scheme and derive an optimal
convergence result with $O(\tau^2+h^{r+1})$ for smooth solutions, where $\tau$
is the time mesh size and $h$ is the spatial mesh size. Some numerical
experiments with smooth and nonsmooth solutions are conducted to confirm our
theoretical analysis. To overcome the singularity at initial value, the
starting part is added to restore the second-order convergence rate in time.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph