Solving Wentzell-Dirichlet Boundary Value Problem with Superabundant Data Using Reflecting Random Walk Simulation

J.-P. Morillon ()
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J.-P. Morillon: Université de La Réunion

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 697-719

Abstract: Abstract In this paper, we are interested in numerical solution of some linear boundary value problems with Wentzell’s boundary part and superabundant data on this part, by the means of simulation of reflected random walks. We use a probabilistic interpretation of solution, assuming that the diffusion coefficient and the boundary data are sufficiently smooth, and applying Itô’s formula. From this stochastic representation of solution, we extend the algorithm obtained for mixed standard boundary conditions to the case of diffusion-reflection on the boundary, so called Wentzell’s boundary condition. We then obtain numerical results by applying the stochastic method based upon this generalized algorithm.

Keywords: Monte Carlo method for linear BVP; Wentzell boundary condition; Reflected diffusion; Probabilistic representation; Stochastic numerical method; 90-08; 90C-15 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9390-3

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