# StochasticDelayDiffEq having trouble with stiff models \[solved\]

**URL:** <https://discourse.julialang.org/t/stochasticdelaydiffeq-having-trouble-with-stiff-models-solved/121725>\
**Category:** Modelling & Simulations\
**Tags:** question, differentialequation\
**Created:** [October 25, 2024, 3:01am UTC](https://discourse.julialang.org/t/stochasticdelaydiffeq-having-trouble-with-stiff-models-solved/121725 "2024-10-25T03:01:31Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![kmd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kmd/32/212868_2.png) [@kmd](https://discourse.julialang.org/u/kmd)\
**Post date:** [October 25, 2024, 3:01am UTC](https://discourse.julialang.org/t/stochasticdelaydiffeq-having-trouble-with-stiff-models-solved/121725/1 "2024-10-25T03:01:32Z")

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I am using SciML to try to integrate a stiff model with small noise. It is giving me tons of grief though, and I am not sure how to approach it. I even tried setting tolerances to very small values & increasing maxiter to several orders of magnitude above the default.  
As a test, I attempted to integrate it using zero noise, since I know the deterministic system can be integrated stably. However, as soon as I switch from the deterministic system with AutoVern7(Rodas5()) to the system with zero noise amplitude using ImplicitRKMil() or SKenCarp() it interrupts the integration.  
With ImplicitRKMil() I get an error like: Interrupted. Larger maxiters is needed.  
With SKenCarp(): At t=1843.1833699767562, dt was forced below floating point epsilon 1.1758922554404307e-13, and step error estimate = 0.20233022763024602. Aborting. There is either an error in your model specification or the true solution is unstable.

Here is an MWE:

```

using DifferentialEquations
using StochasticDelayDiffEq
using Plots
const w=[-0.0974439293080174, -0.0972907033232282, 0.05008580780639362, 31.382671443379348, 1.1925811288818222, 45.142984062837634]
function eqns!(du,u,h,p,t)
	global w
	eps1=0.09
	eps2=0.003
	FREQ=0.9	
	delta=p[1]
        CNORM=2.0*pi/FREQ
	u1 =u[1]
	u2 = u[2]
	du[1]=CNORM*(u2 - delta*cos(2*pi*t + pi/2))
	du[2]=CNORM*(1.0 - eps1*u2 - exp(u1) - eps2*exp(u1)*u2)
	du[1]+=w[1]*h(p,t-w[4])[1]+w[2]*h(p,t-w[5])[1]+w[3]*h(p,t-w[6])[1]
	du[2]+=w[1]*h(p,t-w[4])[2]+w[2]*h(p,t-w[5])[2]+w[3]*h(p,t-w[6])[2]
end
function g!(du,u,h,p,t)
	du[1]=p[2]*cos.(2.0*pi*t)
	du[2]=0
end
#this works fine.  
h_=function(p,t) [-5.7734959978E+01,4.6557062215E-01] end
stable_problem = DDEProblem(eqns!, h_(0,0),h_, (0.0,5000), (6.08,0);
			    constant_lags = (w[4],w[5],w[6]),dependent_lags=[]
		)
alg=MethodOfSteps(AutoVern7(Rodas5()))
sol=solve(stable_problem,alg,dense=true)
png(plot(sol),"stable.png") #these results are sensible
#this fails at time t=1843.1833... with a dt forced below floating point epsilon warning
#note that the noise amplitude is zero
#if I increase the noise slightly, it is the same thing.
same_problem = SDDEProblem(eqns!, g!, h_(0,0), h_, (0.0,5000), (6.08,0);
			   constant_lags = (w[4],w[5],w[6]),dependent_lags=[])
#this tells me I need larger maxiters and then fails also
new_alg=SKenCarp()
sol2=solve(same_problem,new_alg,dense=false,saveat=0.01)
png(plot(sol2), "unstable.png") #if I decrease the integration time to 1000 this will produce some sort of nonempty figure, but it's way off
another_alg=ImplicitRKMil()
sol3=solve(same_problem,another_alg,dense=false,saveat=0.01)
png(plot(sol3), "unstable2.png") 

```

Any ideas?

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**Author:** ![kmd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kmd/32/212868_2.png) [@kmd](https://discourse.julialang.org/u/kmd)\
**Post date:** [October 25, 2024, 3:26am UTC](https://discourse.julialang.org/t/stochasticdelaydiffeq-having-trouble-with-stiff-models-solved/121725/2 "2024-10-25T03:26:21Z")

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Solved by using the SROCK1() solver, per [Solving stiff SDDE problems · Issue #1 · SciML/StochasticDelayDiffEq.jl · GitHub](https://github.com/SciML/StochasticDelayDiffEq.jl/issues/1)

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<div class="post-metadata">

**Author:** ![kmd](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kmd/32/212868_2.png) [@kmd](https://discourse.julialang.org/u/kmd)\
**Post date:** [October 26, 2024, 7:58pm UTC](https://discourse.julialang.org/t/stochasticdelaydiffeq-having-trouble-with-stiff-models-solved/121725/3 "2024-10-26T19:58:14Z")

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Just a quick final update that the implicit solvers appear to be working with StochasticDelayDiffEq. I just had to set dtmin a bit lower to avoid error. Actually, they work better than SROCK1 for this case.