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Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

Published 24 Dec 2015 in math.NA, math.AP, and math.PR | (1512.07725v1)

Abstract: We show that a constant-potential time-independent Schr\"odinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

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