NUMERICAL SOLUTIONS OF LINEAR MIXED BOUNDARY VALUE PROBLEMS USING STOCHASTIC REPRESENTATIONS

Jean-Paul Morillon (1)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

The application of Itô's formula induces some probabilistic representations of solutions of deterministic linear problems with boundary conditions of Dirichlet, Neumann, Fourier and mixed types. These representations are used to establish some easily implementable algorithms which compute an approximate solution by means of simulation of reflected random walks. They do not require selected configurations at the neighbourhood of the domain boundary, nor a discretization mesh. The associated simulation methods are obtained and applied to problems for each class of boundary conditions. Numerical experiments with distributed source in two- or three-dimensional geometries, and computational results with estimation of error, are reported. © 1997 by John Wiley & Sons, Ltd.

Mots clés: deterministic PDE; boundary value problems; probabilistic interpretations; stochastic methods; mixed boundary conditions; random walks

Domaines: Probabilités [math.PR]

Jean-Paul Morillon. NUMERICAL SOLUTIONS OF LINEAR MIXED BOUNDARY VALUE PROBLEMS USING STOCHASTIC REPRESENTATIONS. International Journal for Numerical Methods in Engineering, 1997, 40 (3), pp.387-405. ⟨10.1002/(SICI)1097-0207(19970215)40:3<387::AID-NME69>3.0.CO;2-D⟩. ⟨hal-00967554⟩