Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An IMEX-RK scheme for capturing similarity solutions in the
  multidimensional Burgers' equation   In this paper we introduce a new, simple and efficient numerical scheme for
the implementation of the freezing method for capturing similarity solutions in
partial differential equations. The scheme is based on an IMEX-Runge-Kutta
approach for a method of lines (semi-)discretization of the freezing partial
differential algebraic equation (PDAE). We prove second order convergence for
the time discretization at smooth solutions in the ODE-sense and we present
numerical experiments that show second order convergence for the full
discretization of the PDAE. As an example serves the multi-dimensional Burgers'
equation. By considering very different sizes of viscosity, Burgers' equation
can be considered as a prototypical example of general coupled
hyperbolic-parabolic PDEs. Numerical experiments show that our method works
perfectly well for all sizes of viscosity, suggesting that the scheme is indeed
suitable for capturing similarity solutions in general hyperbolic-parabolic
PDEs by direct forward simulation with the freezing method.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con