Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: R\'esolution num\'erique du probl\`eme de Dirichlet $\Delta u = a\,u^3$
  \`a l'aide du mouvement brownien   In this paper, we are interested in numerical solution of some linear
boundary value problems with Dirichlet boundary part, by the means of
simulation of random walks. We use a probabilistic interpretation of solution
$u$, assuming that the coefficient and the boundary data are sufficiently
smooth, and applying It\^o's formula. From these stochastic representations of
solution, we extend some algorithms obtained for standard boundary conditions
to the quasi-linear source of the type $f(u)= a\,u^3$. For positive and
negative parameter $a$, we then obtain numerical results by applying the
stochastic methods based upon these generalized algorithms.

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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol