Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order accurate numerical scheme with graded meshes for the
  nonlinear partial integrodifferential equation arising from viscoelasticity   This paper establishes and analyzes a second-order accurate numerical scheme
for the nonlinear partial integrodifferential equation with a weakly singular
kernel. In the time direction, we apply the Crank-Nicolson method for the time
derivative, and the product-integration (PI) rule is employed to deal with
Riemann-Liouville fractional integral. From which, the non-uniform meshes are
utilized to compensate for the singular behavior of the exact solution at $t=0$
so that our method can reach second-order convergence for time. In order to
formulate a fully discrete implicit difference scheme, we employ a standard
centered difference formula for the second-order spatial derivative, and the
Galerkin method based on piecewise linear test functions is used to approximate
the nonlinear convection term. Then we derive the existence and uniqueness of
numerical solutions for the proposed implicit difference scheme. Meanwhile,
stability and convergence are proved by means of the discrete energy method.
Furthermore, to demonstrate the effectiveness of the proposed method, we
utilize a fixed point iterative algorithm to calculate the discrete scheme.
Finally, numerical experiments illustrate the feasibility and efficiency of the
proposed scheme, in which numerical results are consistent with our theoretical
analysis.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga