Stochastic Simulation of Diffusion with Absorbing and Reflecting Boundary Conditions

16 Pages Posted: 5 May 2020

See all articles by Roland Lichters

Roland Lichters

Quaternion Risk Management

Thomas Fricke

affiliation not provided to SSRN

Jürgen Schnakenberg

affiliation not provided to SSRN

Date Written: January 4, 1995

Abstract

We present an algorithm for simulating diffusion of particles in the presence of absorbing or reflecting boundaries. The algorithm is based up on the exact solution of the first passage time problem for a particle to arrive at the surface of a sphere (for d=3) or disc (for d=2) after having been started in its center. The simulation steps are taken to be diffusion jumps within maximal spheres (discs) which are centered in the particle's present position and touch the nearest boundary. The use of the exact solution of the first passage time problem enables us to evaluate all kinds of probability densities without approximations or systematic errors up to any desired accuracy. The algorithm is applied to absorbing spheres (discs) in d=3 and d=2 and to reflecting discs in d=2 for regular and random positions of the spheres (discs).

Suggested Citation

Lichters, Roland and Fricke, Thomas and Schnakenberg, Jürgen, Stochastic Simulation of Diffusion with Absorbing and Reflecting Boundary Conditions (January 4, 1995). Available at SSRN: https://ssrn.com/abstract=3570551 or http://dx.doi.org/10.2139/ssrn.3570551

Roland Lichters (Contact Author)

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Thomas Fricke

affiliation not provided to SSRN

Jürgen Schnakenberg

affiliation not provided to SSRN

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