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Topic: Stochastic differential equations with Simulink?
Replies: 4   Last Post: Aug 29, 2013 8:15 AM

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 Phil Goddard Posts: 358 Registered: 1/27/12
Re: Stochastic differential equations with Simulink?
Posted: Aug 6, 2013 10:36 AM

> I*A''(t)=m*g*h*A(t)-[P1*A(t)+D1*A'(t)+f1(A(t-d))+f2(A'(t-d))]+s*n(t),
>
> f1(A(t-d))=P2*A(t-d) & f2(A'(t-d))=D2*A'(t-d), when A(t-d)*[A'(t-d)-a*A(t-d)]>0 and
> f1(A(t-d))=0 & f2(A'(t-d))=0 otherwise.

Isn't the above just a non-linear ODE with Gaussian noise?
In which case it's relatively simple to implement.

>
> x(n+1)=x(n)+f(x(n),x(n-k))dt+s*n(t)*sqrt(dt)
> k=d/dt. The initial state is x0=[A(0),A'(0)]=[0.01,0].

I don't understand the term k=d/dt (a time delay specified as a partial derivative?), but in general if you use a fixed step solver then you know dt in advance and the sqrt(dt) term is just a (constant) modifier to the variance of the noise.

Phil.

Date Subject Author
8/6/13 Tikkuhirvi Tietavainen
8/6/13 Phil Goddard
8/6/13 Phil Goddard
8/7/13 Tikkuhirvi Tietavainen
8/29/13 Tikkuhirvi Tietavainen