Summary
Elliptic boundary value problem (BVP) for the stationary diffusion equation is considered. Within [BM03], we estimate the solution and its spatial derivatives by solving a system of local integral equations. We propose to use the Poisson-Boltzmann Green function instead of the Laplacian one. This enables us to obtain a convergent Neumann series for a wider class of equations.
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Burmistrov, A. (2008). Random Walk Algorithm for Estimating the Derivatives of Solution to the Elliptic BVP. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_9
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DOI: https://doi.org/10.1007/978-3-540-74496-2_9
Publisher Name: Springer, Berlin, Heidelberg
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