Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the generalized method of lines and its proximal explicit and
  hyper-finite difference approaches   This article firstly develops a proximal explicit approach for the
generalized method of lines. In such a method, the domain of the PDE in
question is discretized in lines and the equation solution is written on these
lines as functions of the boundary conditions and domain shape. The main
objective of introducing a proximal formulation is to minimize the solution
error as a typical parameter $\varepsilon>0$ is too small. In a second step we
present another procedure to minimize this same error, namely, the hyper-finite
differences approach. In this last method the domain is divided in sub-domains
on which the solution is obtained through the generalized method of lines
allowing the parameter $\varepsilon>0$ to be very small without increasing the
solution error. The solutions for the sub-domains are connected through the
boundary conditions and the solution of the partial differential equation in
question on the node lines which separate the sub-domains. In the last sections
of each text part we present the concerning softwares and perform numerical
examples.

33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg