# Extracting derivatives (du/dt) from an ODE problem

**URL:** <https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514>\
**Category:** Modelling & Simulations\
**Tags:** question, diffeq\
**Created:** [July 18, 2019, 7:23pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514 "2019-07-18T19:23:25Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 18, 2019, 7:23pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/1 "2019-07-18T19:23:26Z")

</div>

I have multiple ODE problems that I am solving. where I need the solutions (u) and derivative of the solutions (du). For smaller ODEs it is practical for me to do the following

```julia
using DifferentialEquations

function SB(du,u,p,t)
    du[1]=@. u[2]
    du[2]=@. ((-0.5*u[2]^2)*(3-u[2]/(p[4]))+(1+(1-3*p[7])*u[2]/p[4])*((p[6]-p[5])/p[2]+2*p[1]/(p[2]*p[9]))*(p[9]/u[1])^(3*p[7])-2*p[1]/(p[2]*u[1])-4*p[3]*u[2]/(p[2]*u[1])-(1+u[2]/p[4])*(p[6]-p[5]+p[10]*sin(2*pi*p[8]*t))/p[2]-p[10]*u[1]*cos(2*pi*p[8]*t)*2*pi*p[8]/(p[2]*p[4]))/((1-u[2]/p[4])*u[1]+4*p[3]/(p[2]*p[4]))
end

R0=2e-6
ps=250e3
f=2e6

u0=([R0 0])
tspan=(0,100/f)

p=[0.0725, 998, 1e-3,1481, 0, 1.01e5,7/5,f, R0, ps]

prob = ODEProblem(SB,u0,tspan,p)
@time u = solve(prob,Tsit5(),alg_hints=[:stiff],saveat=0.01/f,reltol=1e-8,abstol=1e-8)
t=u.t
u2=@. ((-0.5*u[2,:]^2)*(3-u[2,:]/(p[4]))+(1+(1-3*p[7])*u[2,:]/p[4])*((p[6]-p[5])/p[2]+2*p[1]/(p[2]*p[9]))*(p[9]/u[1,:])^(3*p[7])-2*p[1]/(p[2]*u[1,:])-4*p[3]*u[2,:]/(p[2]*u[1,:])-(1+u[2,:]/p[4])*(p[6]-p[5]+p[10]*sin(2*pi*p[8]*t))/p[2]-p[10]*u[1,:]*cos(2*pi*p[8]*t)*2*pi*p[8]/(p[2]*p[4]))/((1-u[2,:]/p[4])*u[1,:]+4*p[3]/(p[2]*p[4]))

```

where u2 is bascially du[2] in the SB function. This quickly becomes impractical as the size of my ODEs grow (\>500 coupled ODEs with \>500X500 matrices). Is there way to ask DifferentialEquations.jl package (or any other way) to export du[i]s as it is solving the ODEs? as a side note, it is important to mention that i need every time step that I am asking the solver to save the output at (saveat=0.01/f). I learned that using `integrator` and `get_du!` I should be able to do the job.

```nohighlight
Rdot=zeros(50001,2)
u = init(prob,SSPRK22(),dt=1e-9,reltol=1e-8,abstol=1e-8)
solve!(u)
get_du!(Rdot,u)

```

However the obtained results from get\_du! do not match u2. Am I missing something? appreciate the help.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [July 18, 2019, 7:32pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/2 "2019-07-18T19:32:13Z")

</div>

> [@Hossein\_Haghi](#):
>
> Is there way to ask DifferentialEquations.jl package (or any other way) to export du[i]s as it is solving the ODEs?

Yes, using the `SavingCallback`, as described in the link at StackOverflow:

> <https://stackoverflow.com/questions/57012586/extracting-derivatives-du-dt-from-an-ode-problem/57018480#57018480>

Here’s the same example, but now saving the `du`s out:

```julia
using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra
prob = ODEProblem((du,u,p,t) -> du .= u, rand(4), (0.0,1.0))
saved_values = SavedValues(Float64, Vector{Float64})
cb = SavingCallback((u,t,integrator)->(get_du(integrator), saved_values)
sol = solve(prob, Tsit5(), callback=cb)

```

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 18, 2019, 8:43pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/3 "2019-07-18T20:43:23Z")

</div>

I am trying to run this as an example

```julia
using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra
prob = ODEProblem((du,u,p,t) -> du .= u, rand(4), (0.0,1.0))
saved_values = SavedValues(Float64, Vector{Float64})
cb = SavingCallback((u,t,integrator)->(get_du(integrator), saved_values)
sol = solve(prob, Tsit5(), callback=cb)

```

and expanding it to my code but I am not entirely sure what the error message means by this

```julia
UndefRefError: access to undefined reference
in expression starting at untitled:5

```

line 5 is `sol = solve(prob, Tsit5(), callback=cb)`

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [July 19, 2019, 1:45am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/4 "2019-07-19T01:45:46Z")

</div>

```julia
using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra
prob = ODEProblem((du,u,p,t) -> du .= u, rand(4), (0.0,1.0))
saved_values = SavedValues(Float64, Vector{Float64})
cb = SavingCallback((u,t,integrator)->get_du(integrator), saved_values, saveat = 0.1:0.1:1.0)
sol = solve(prob, Tsit5(), callback=cb)
saved_values

```

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 19, 2019, 6:47pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/5 "2019-07-19T18:47:55Z")

</div>

> [@ChrisRackauckas](#):
>
> using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra prob = ODEProblem((du,u,p,t) → du .= u, rand(4), (0.0,1.0)) saved\_values = SavedValues(Float64, Vector{Float64}) cb = SavingCallback((u,t,integrator)-\>get\_du(integrator), saved\_values, saveat = 0.1:0.1:1.0) sol = solve(prob, Tsit5(), callback=cb) saved\_values

I tried the above suggested example and also used it in my problem as

```julia

using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra
function SB(du,u,p,t)
    du[1]=@. u[2]
    du[2]=@. ((-0.5*u[2]^2)*(3-u[2]/(p[4]))+(1+(1-3*p[7])*u[2]/p[4])*((p[6]-p[5])/p[2]+2*p[1]/(p[2]*p[9]))*(p[9]/u[1])^(3*p[7])-2*p[1]/(p[2]*u[1])-4*p[3]*u[2]/(p[2]*u[1])-(1+u[2]/p[4])*(p[6]-p[5]+p[10]*sin(2*pi*p[8]*t))/p[2]-p[10]*u[1]*cos(2*pi*p[8]*t)*2*pi*p[8]/(p[2]*p[4]))/((1-u[2]/p[4])*u[1]+4*p[3]/(p[2]*p[4]))
end

R0=2e-6
ps=250e3
f=2e6

u0=([R0 0])
tspan=(0,100/f)

p=[0.0725, 998, 1e-3,1481, 0, 1.01e5,7/5,f, R0, ps]

prob = ODEProblem(SB,u0,tspan,p)
saved_values = SavedValues(Float64, Array{Float64})
cb = SavingCallback((u,t,integrator)->get_du(integrator), saved_values, saveat = 1e-9:1e-9:100/f)
sol =solve(prob,Tsit5(),saveat=1e-9,reltol=1e-8,abstol=1e-8,callback=cb)

```

when I plot `saved_values.saveval`, the values do not change with `t` and are constant in both the provided example and also my code

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 22, 2019, 5:46pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/6 "2019-07-22T17:46:13Z")

</div>

@ChrisRackauckas Can you please take a look at this?

I am migrating all of my codes from MATLAB to Julia and getting du[i]s is one of my main problems. Appreciate the help.

---

<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [July 22, 2019, 6:53pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/7 "2019-07-22T18:53:47Z")

</div>

Is it possible to differentiate the solution interpolation functions? Or…

- non-differentiable interpolation functions
- too inaccurate?

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 22, 2019, 7:15pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/8 "2019-07-22T19:15:43Z")

</div>

You mean like  
(u[i+1]-u[i])/(t[i+1]-t[i]) ?

This usually ends up being too inaccurate (when I used it previously in MATLAB it was very inaccruate), also, the output vector (du[i]s) will have one less data point than the u[i]s.

---

<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [July 22, 2019, 8:13pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/9 "2019-07-22T20:13:58Z")

</div>

No, that’s not what I mean. Observe that `u` has _two_ interpretations:

1. An array, where an element is addressed, e.g., as `u[1]`, etc.
2. An interpolation function addressed as, e.g., `u(1.5)`, i.e., evaluated at time 1.5, which does not need to be an element in the time vector.

If the interpolation function has continuous derivative, and is supported by, e.g., ForwardDiff, you can easily compute the derivative.

Alternatively, if the interpolation function supports imaginary time, you can use the complex Taylor series trick, see e.g., Prof Higham’s discussion in a past JuliaCon.

Don’t know if this is possible (support for AD, or admits imaginary time), and don’t know how accurate it will be.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [July 23, 2019, 12:35am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/10 "2019-07-23T00:35:44Z")

</div>

> [@BLI](#):
>
> If the interpolation function has continuous derivative, and is supported by, e.g., ForwardDiff, you can easily compute the derivative.

The derivative of the interpolation is already hardcoded with `Val{1}` .

```julia
using DiffEqCallbacks, OrdinaryDiffEq, LinearAlgebra
function SB(du,u,p,t)
    du[1]=@. u[2]
    du[2]=@. ((-0.5*u[2]^2)*(3-u[2]/(p[4]))+(1+(1-3*p[7])*u[2]/p[4])*((p[6]-p[5])/p[2]+2*p[1]/(p[2]*p[9]))*(p[9]/u[1])^(3*p[7])-2*p[1]/(p[2]*u[1])-4*p[3]*u[2]/(p[2]*u[1])-(1+u[2]/p[4])*(p[6]-p[5]+p[10]*sin(2*pi*p[8]*t))/p[2]-p[10]*u[1]*cos(2*pi*p[8]*t)*2*pi*p[8]/(p[2]*p[4]))/((1-u[2]/p[4])*u[1]+4*p[3]/(p[2]*p[4]))
end

R0=2e-6
ps=250e3
f=2e6

u0=([R0 0])
tspan=(0,100/f)

p=[0.0725, 998, 1e-3,1481, 0, 1.01e5,7/5,f, R0, ps]

prob = ODEProblem(SB,u0,tspan,p)
saved_values = SavedValues(Float64, Matrix{Float64})
cb = SavingCallback((u,t,integrator)->integrator(t,Val{1}), saved_values, saveat = 1e-9:1e-9:100/f)
sol =solve(prob,Tsit5(),reltol=1e-8,abstol=1e-8,saveat=1e-9,callback=cb)

saved_values.t
saved_values.saveval

```

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [July 23, 2019, 5:27pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/11 "2019-07-23T17:27:17Z")

</div>

Thanks! this is exactly what I needed!  
In my applications, Julia has been 40-60 times faster than MATLAB so far! Really happy with DifferentialEquations.jl package.

---

<div class="post-metadata">

**Author:** ![donkeysaddle](https://avatars.discourse-cdn.com/v4/letter/d/3e96dc/32.png) [@donkeysaddle](https://discourse.julialang.org/u/donkeysaddle)\
**Post date:** [April 2, 2020, 2:05am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/12 "2020-04-02T02:05:31Z")

</div>

@ChrisRackauckas,  
Is this still that best way to do this? The corresponding documentation pages linked in the StackOverflow page no longer exist.

Thanks,

DS

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 2, 2020, 2:07am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/13 "2020-04-02T02:07:12Z")

</div>

Thanks, I fixed the links. Yes, still the same.

---

<div class="post-metadata">

**Author:** ![donkeysaddle](https://avatars.discourse-cdn.com/v4/letter/d/3e96dc/32.png) [@donkeysaddle](https://discourse.julialang.org/u/donkeysaddle)\
**Post date:** [April 6, 2020, 2:35am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/14 "2020-04-06T02:35:01Z")

</div>

Question regarding ` saved_values.saveval` from callback. I have an example, very similar to the one presented by Hossein\_Haghi:

```julia
function model(du,u,p,t)
  du[1] = dx = -(p[1]u[1] + p[2]*u[1])
  du[2] = dy = -p[3]*u[1] - p[4]

end 

tspan = (0.0,500.0) 

u0 = [20.0;5.0]

p = [0.002, 0.0100, 0.0020, 1.71799639e-03]  

prob = ODEForwardSensitivityProblem(model, u0, tspan, p)
saved_values = SavedValues(Float64, Array{Float64})
cb = SavingCallback((u, t, integrator)->integrator(t,Val{1}), saved_values, saveat=0.0:1:500.0)

sol = solve(prob,DP8(),saveat=1,callback=cb)
x,dp = extract_local_sensitivities(sol);
saved_values.t
saved_values.saveval

```

What values/derivatives are contained in the arrays of, ` saved_values.saveval`? I know that the first two values of each array are the derivatives with respect to time of u1 and u2, but what are the other 8 values? Is it (du/dp)/dt, for each u and p?

Is there a way to just get the derivatives of the u’s w.r.t time and not the other values?

Thanks,

DS

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 6, 2020, 2:45am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/15 "2020-04-06T02:45:56Z")

</div>

> [@donkeysaddle](#):
>
> I know that the first two values of each array are the derivatives with respect to time of u1 and u2, but what are the other 8 values? Is it (du/dp)/dt, for each u and p?

Yup that’s exactly what they are.

> [@donkeysaddle](#):
>
> Is there a way to just get the derivatives of the u’s w.r.t time and not the other values?

like du/dt? That’s just `integrator(t,Val{1})`, or `sol(t,Val{1})` depending on which interface.

---

<div class="post-metadata">

**Author:** ![donkeysaddle](https://avatars.discourse-cdn.com/v4/letter/d/3e96dc/32.png) [@donkeysaddle](https://discourse.julialang.org/u/donkeysaddle)\
**Post date:** [April 6, 2020, 3:02am UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/16 "2020-04-06T03:02:24Z")

</div>

Thanks so much.

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [April 6, 2020, 10:18pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/17 "2020-04-06T22:18:49Z")

</div>

I am trying to the same thing but for higher orders of d/dt for my du[1] and du[2] in function as follows

```julia
function SB(du,u,p,t)
    du[1]=@. u[2]
    du[2]=@. ((-0.5*u[2]^2)*(3-u[2]/(p[4]))+(1+(1-3*p[7])*u[2]/p[4])*((p[6]-p[5])/p[2]+2*p[1]/(p[2]*p[9]))*(p[9]/u[1])^(3*p[7])-2*p[1]/(p[2]*u[1])-4*p[3]*u[2]/(p[2]*u[1])-(1+u[2]/p[4])*(p[6]-p[5]+p[10]*sin(2*pi*p[8]*t))/p[2]-p[10]*u[1]*cos(2*pi*p[8]*t)*2*pi*p[8]/(p[2]*p[4]))/((1-u[2]/p[4])*u[1]+4*p[3]/(p[2]*p[4]))
end

########################
## Control Parameters ##
########################
ps=100e3
R0=2e-6
f=1e6

u0=([R0 0])

tspan=(0,1e-10)
p=[0.0725, 998, 1e-3,1481, 0, 1.01e5,7/5,f, R0, ps]
prob = ODEProblem(SB,u0,tspan,p)

saved_values = SavedValues(Float64, Array{Float64})
saved_values2=SavedValues(Float64, Array{Float64})
saved_values3=SavedValues(Float64, Array{Float64})
saved_values4=SavedValues(Float64, Array{Float64})
saved_values5=SavedValues(Float64, Array{Float64})
saved_values6=SavedValues(Float64, Array{Float64})
saved_values7=SavedValues(Float64, Array{Float64})

cb1 = SavingCallback((u,t,integrator)->integrator(t,Val{1}), saved_values , saveat = 0:span/f:TT) #R2
cb2 = SavingCallback((u,t,integrator)->integrator(t,Val{2}), saved_values2, saveat = 0:span/f:TT) #R3
cb3 = SavingCallback((u,t,integrator)->integrator(t,Val{3}), saved_values3, saveat = 0:span/f:TT) #R4
cb4 = SavingCallback((u,t,integrator)->integrator(t,Val{4}), saved_values4, saveat = 0:span/f:TT) #R5
cb5 = SavingCallback((u,t,integrator)->integrator(t,Val{5}), saved_values5, saveat = 0:span/f:TT) #R6
cb6 = SavingCallback((u,t,integrator)->integrator(t,Val{6}), saved_values6, saveat = 0:span/f:TT) #R7
cb7 = SavingCallback((u,t,integrator)->integrator(t,Val{7}), saved_values7, saveat = 0:span/f:TT) #R8

@time u = solve(prob,Tsit5(),saveat=1e-12,reltol=1e-12,abstol=1e-12,callback=CallbackSet(cb1,cb2,cb3,cb4,cb5))

```

it can go up to cb4 but crashes when I attempt to go to cb5 and higher returning the following error

```julia
MethodError: no method matching hermite_interpolant!(::Array{Float64,2}, ::Float64, ::Float64, ::Array{Float64,2}, ::Array{Float64,2}, ::Array{Array{Float64,2},1}, ::Nothing, ::Type{Val{5}})
Closest candidates are:
  hermite_interpolant!(::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Nothing, !Matched::Type{Val{0}}) at C:\Users\The Hossein\.julia\packages\OrdinaryDiffEq\8Pn99\src\dense\generic_dense.jl:419
  hermite_interpolant!(::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Any, !Matched::Type{Val{0}}) at C:\Users\The Hossein\.julia\packages\OrdinaryDiffEq\8Pn99\src\dense\generic_dense.jl:427
  hermite_interpolant!(::Any, ::Any, ::Any, ::Any, ::Any, ::Any, ::Nothing, !Matched::Type{Val{1}}) at C:\Users\The Hossein\.julia\packages\OrdinaryDiffEq\8Pn99\src\dense\generic_dense.jl:452

```

Can you please advice how to go to higher d/dts?  
I basically only need these values for higher du/dt at t=0 as initial conditions for another DDE I am trying to solve.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 6, 2020, 10:37pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/18 "2020-04-06T22:37:00Z")

</div>

> [@Hossein\_Haghi](#):
>
> Can you please advice how to go to higher d/dts?

You need to use a method with a really high order interpolation. Directly choose `Vern9` for this. `Tsit5` only has a 4th order interpolation, so it’s failing at 5 derivatives of the interpolant. I don’t know if we’ve hardcoded all 9 derivatives though, but if you need it, I could show you what PR to make. It’s not hard, just tedious.

---

<div class="post-metadata">

**Author:** ![Hossein\_Haghi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hossein_haghi/32/9413_2.png) [@Hossein\_Haghi](https://discourse.julialang.org/u/Hossein_Haghi)\
**Post date:** [April 6, 2020, 10:52pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/19 "2020-04-06T22:52:15Z")

</div>

I could certainly try if you show me how to do it.

it is still failing at `cb5` with `Vern9`

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 6, 2020, 10:52pm UTC](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514/20 "2020-04-06T22:52:20Z")

</div>

We’ve only written out the first 4 derivatives of the polynomial, but we put it in a style where it’s clear how to do it:

> <https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/dense/interpolants.jl#L1785-L1842>

Just need a soldier to make the next 4

[Next page](https://discourse.julialang.org/t/extracting-derivatives-du-dt-from-an-ode-problem/26514.md?page=2)