Difference between revisions of "Walk-on-spheres method"
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In [[mathematics]], the '''walk-on-spheres method''' (WoS) is a numerical probabilistic algorithm, or [[Monte-Carlo method]], used mainly in order to approximate the solutions of some specific boundary value problem for [[Partial differential equation|partial differential equations]]. | In [[mathematics]], the '''walk-on-spheres method''' (WoS) is a numerical probabilistic algorithm, or [[Monte-Carlo method]], used mainly in order to approximate the solutions of some specific boundary value problem for [[Partial differential equation|partial differential equations]]. | ||
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The WoS method was first introduced by [[M. E. Muller]] in 1956 to solve [[Laplace's equation]], and was since then generalized to other problems. | The WoS method was first introduced by [[M. E. Muller]] in 1956 to solve [[Laplace's equation]], and was since then generalized to other problems. | ||
Latest revision as of 14:24, 23 April 2016
In mathematics, the walk-on-spheres method (WoS) is a numerical probabilistic algorithm, or Monte-Carlo method, used mainly in order to approximate the solutions of some specific boundary value problem for partial differential equations.
Description
The WoS method was first introduced by M. E. Muller in 1956 to solve Laplace's equation, and was since then generalized to other problems.
It relies on probabilistic interpretations of PDEs, by simulating paths of Brownian motion (or for some more general variants, diffusion processes), and it is today one of the most widely used "grid-free" algorithms for generating Brownian paths.
