Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stability and Convergence of a Three-layer Semi-discrete Scheme for
  an Abstract Analogue of the Ball Integro-differential Equation   We consider the Cauchy problem for a second-order nonlinear evolution
equation in a Hilbert space. This equation represents the abstract
generalization of the Ball integro-differential equation. The general nonlinear
case with respect to terms of the equation which include a square of a norm of
a gradient is considered. A three-layer semi-discrete scheme is proposed in
order to find an approximate solution. In this scheme, the approximation of
nonlinear terms that are dependent on the gradient is carried out by using an
integral mean. We show that the solution of the nonlinear discrete problem and
its corresponding difference analogue of a first-order derivative is uniformly
bounded. For the solution of the corresponding linear discrete problem, it is
obtained high-order a priori estimates by using two-variable Chebyshev
polynomials. Based on these estimates we prove the stability of the nonlinear
discrete problem. For smooth solutions, we provide error estimates for the
approximate solution. An iteration method is applied in order to find an
approximate solution for each temporal step. The convergence of the iteration
process is proved.

0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat