Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic solutions of Stefan problems   This work deals with the one-dimensional Stefan problem with a general
time-dependent boundary condition at the fixed boundary. Stochastic solutions
are obtained using discrete random walks, and the results are compared with
analytic formulae when they exist, otherwise with numerical solutions from a
finite difference method. The innovative part is to model the moving boundary
with a random walk method. The results show statistical convergence for many
random walkers when $\Delta x \rightarrow 0$. Stochastic methods are very
competitive in large domains in higher dimensions and has the advantages of
generality and ease of implementation. The stochastic method suffers from that
longer execution times are required for increased accuracy. Since the code is
easily adapted for parallel computing, it is possible to speed up the
calculations. Regarding applications for Stefan problems, they have
historically been used to model the dynamics of melting ice, and we give such
an example here where the fixed boundary condition follows data from observed
day temperatures at \"{O}rebro airport. Nowadays, there are a large range of
examples of applications, such as climate models, the diffusion of lithium-ions
in lithium-ion batteries and modelling steam chambers for petroleum extraction.

8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con