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I am trying to simulate a stochastic differential equation in time and space, but I'm unsure if this can be done in Mathematica. The sde that I would like to study is:

$$ dN[x,t]=N[x,t](1-N[x,t])dt+\sqrt{N[x,t]}dw+\partial^2_xN[x,t]dt $$

With an exponential decreasing (in space) initial condition N[x,0]=Exp[-|x|]. Is this possible to simulate with ItoProcess?

Thank you, Best, Andrea

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it can be done, for example, by discretising spatially. –  acl Apr 12 '13 at 10:22
    
Sorry but I don't see easily how, in particular I feel I would have no control on step sizes in time –  Andrea Apr 13 '13 at 8:56
1  
discretize spatially, this solving a set of coupled SDEs in time. like the method of lines for PDEs. –  acl Apr 13 '13 at 9:15

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