> 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.