http://wiki.karljones.com/index.php?action=history&feed=atom&title=Walk-on-spheres_method 2026-10-23T21:55:00Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Walk-on-spheres_method&diff=12987&oldid=prev 2016-04-23T20:24:39Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:24, 23 April 2016</td> </tr><tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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]].</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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]].</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Description ==</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr> </table>

Karl Jones http://wiki.karljones.com/index.php?title=Walk-on-spheres_method&diff=12986&oldid=prev 2016-04-23T20:24:22Z

<p>Created page with &quot;In <a href="/index.php/Mathematics" title="Mathematics">mathematics</a>, the &#039;&#039;&#039;walk-on-spheres method&#039;&#039;&#039; (WoS) is a numerical probabilistic algorithm, or <a href="/index.php?title=Monte-Carlo_method&amp;action=edit&amp;redlink=1" class="new" title="Monte-Carlo method (page does not exist)">Monte-Carlo method</a>, used mainly in order to approximate the solutions...&quot;</p> <p><b>New page</b></p><div>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]].<br /> <br /> 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.<br /> <br /> 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 &quot;grid-free&quot; algorithms for generating Brownian paths.<br /> <br /> == See also ==<br /> <br /> * [[Mathematics]]<br /> * [[Monte-Carlo method]]<br /> * [[Partial differential equation]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Walk-on-spheres_method Walk-on-spheres method]<br /> <br /> [[Category:Mathematics]]</div>

Karl Jones