2013/04/16 by Jean-Paul Morillon, Morillon, Jean-Paul
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR
paper · pdf · doi:10.48550/arxiv.1304.4374
in French
arxiv created 2013/04/16 · openalex publication_date 2013/04/16 · arxiv updated 2013/04/17 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28
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 Itô'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 u3. For positive and negative parameter a, we then obtain numerical results by applying the stochastic methods based upon these generalized algorithms.