# solve a stochastic partial differential equation

Every example about solving a stochastic differential equation uses an ordinary differential equation (derivatives with respect to one variable), but ¿what about solving this when de function depends on two or three variables and you have derivatives with respect to time (of course) and second derivatives with respect to space variables?

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Perhaps a confusion between Mathematica.SE and Mathematics.SE? –  mac389 Dec 25 '13 at 2:36
@andre. Don't forget Mathematica has stuff on board for stochastic differential equations. –  Sjoerd C. de Vries Dec 25 '13 at 8:47
Could you please give some concrete examples? As how I understand the documentation of ItoProcess, Mathematica cannot handle space derivate in it directly, but it may be achieved other way. –  Silvia Dec 25 '13 at 13:06
@silvia How about the 10th and further examples under Scope/Basic Uses on that page? Don't know much about spde's, but this looks like we're dealing with two spatial coordinates. –  Sjoerd C. de Vries Dec 25 '13 at 13:27
@SjoerdC.deVries I'm not familiar with SPDE either, but I think those look quite promising. Not sure whether it can handle complicated cases sophisticatedly. –  Silvia Dec 25 '13 at 13:51

## 1 Answer

I believe you could use something like the method of lines to approximate your stochastic PDE by a system of SDEs, which you can then solve in the usual way. See e.g. this paper for a proof that the method of lines can be validly applied to SPDEs.

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This isn't an answer. At east not for this site. –  belisarius Dec 25 '13 at 4:06
Hi Ilmari, could you consider extend your answer with some examples and codes, which will make it more clear and applicable. –  Silvia Dec 25 '13 at 13:10
@Silvia: Alas, no. I do have some old Mathematica code for numerically solving SDEs that I could probably adapt with some effort, but I don't have either the code or Mathematica on this computer. And I pretty much agree with belisarius: neither my answer nor the original question have much to do with Mathematica specifically. I did consider making this just a comment, but since I did more or less answer the question asked, I figured it should be an answer, even if it's not a very good one. –  Ilmari Karonen Dec 25 '13 at 13:54