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

Xuxin Yang, Antti Rasila () and Tommi Sottinen
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Xuxin Yang: Hunan First Normal University
Antti Rasila: Aalto University
Tommi Sottinen: University of Vaasa

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 2, 589-602

Abstract: Abstract We show that a constant-potential time-independent Schrödinger 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.

Keywords: Brownian motion; Helmholtz equation; Linearized Poisson–Boltzmann equation; Monte Carlo simulation; Numerical algorithm; Walk On Spheres algorithm; Yukawa equation; 65C05; 68U20; 35Q40 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-016-9504-9

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