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In this paper, we are interested in numerical solution of some linearboundary value problems with Dirichlet boundary part, by the means ofsimulation of random walks. We use a probabilistic interpretation of solution$u$, assuming that the coefficient and the boundary data are sufficientlysmooth, and applying It\^o's formula. From these stochastic representations ofsolution, we extend some algorithms obtained for standard boundary conditionsto the quasi-linear source of the type $f(u)= a\,u^3$. For positive andnegative parameter $a$, we then obtain numerical results by applying thestochastic methods based upon these generalized algorithms.

R\'esolution num\'erique du probl\`eme de Dirichlet $\Delta u = a\,u^3$ \`a l'aide du mouvement brownien