Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-based numerical approximation of the Weertman equation for
  moving dislocations   This work discusses the numerical approximation of a nonlinear
reaction-advection-diffusion equation, which is a dimensionless form of the
Weertman equation. This equation models steadily-moving dislocations in
materials science. It reduces to the celebrated Peierls-Nabarro equation when
its advection term is set to zero. The approach rests on considering a
time-dependent formulation, which admits the equation under study as its
long-time limit. Introducing a Preconditioned Collocation Scheme based on
Fourier transforms, the iterative numerical method presented solves the
time-dependent problem, delivering at convergence the desired numerical
solution to the Weertman equation. Although it rests on an explicit
time-evolution scheme, the method allows for large time steps, and captures the
solution in a robust manner. Numerical results illustrate the efficiency of the
approach for several types of nonlinearities.

14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin