I am trying to solve the following SDE:

du=f(u,p,t)dt+\sigma dW,

where f(u,p,t) can be written as following:

```
function f(du,u,p,t)
#calculate the derivative of the vector at time j
p=0.0
for i=1:Nx
if i==2
du[i]=-(u[i+1]^2-0)/(4*Δx)-p*(u[i+1]-0)/(2*Δx)-(u[i+1]-2*u[i]+0)/(Δx^2)-(u[i]-0+6*u[i]-4*u[i+1]+u[i+2])/(Δx^4)
end
if i==3
du[i]=-(u[i+1]^2-u[i-1]^2)/(4*Δx)-p*(u[i+1]-u[i-1])/(2*Δx)-(u[i+1]-2*u[i]+u[i-1])/(Δx^2) -(0-4*u[i-1]+6*u[i]-4*u[i+1]+u[i+2])/(Δx^4)
end
if i>=4 && i<=Nx-3 # Inner scheme
du[i]=-(u[i+1]^2-u[i-1]^2)/(4*Δx)-p*(u[i+1]-u[i-1])/(2*Δx)-(u[i+1]-2*u[i]+u[i-1])/(Δx^2) -(u[i-2]-4*u[i-1]+6*u[i]-4*u[i+1]+u[i+2])/(Δx^4)
end
if i==Nx-2 # u[i+2]=0
du[i]=-(u[i+1]^2-u[i-1]^2)/(4*Δx)-p*(u[i+1]-u[i-1])/(2*Δx)-(u[i+1]-2*u[i]+u[i-1])/(Δx^2) -(u[i-2]-4*u[i-1]+6*u[i]-4*u[i+1]+0)/(Δx^4)
end
if i==Nx-1
du[i]=-(0-u[i-1]^2)/(4*Δx)-p*(0-u[i-1])/(2*Δx)-(0-2*u[i]+u[i-1])/(Δx^2)-(u[i-2]-4*u[i-1]+6*u[i]-0+u[i])/(Δx^4)
end
end
return du
end
```

and \sigma=3.0. In order to do that, I wrote the following code:

```
p = [c] # parameter
Random.seed!(SEED)
u0 =vec(-0.5 * ones(N, 1) + (0.5 + 0.5) * rand(N, 1))
u0[1] = 0.0
u0[end] = 0.0
tspan = (0.0, Tspan)
###############################################################################
function g(du1,u,p,t)
du1=ones(1,N).*3.0
return du1
end
###############################################################################
prob_sde= SDEProblem(f,g, u0, tspan, p)
sol = solve(prob_sde,saveat=Δt)
U = convert(Array, sol)
```

Now I expect that every time I solve this problem without changing anything, I should get a different solution U due to the noise. However, I always get the same solution. Why is that?