# Julia DifferentialEquations for state-to-state binary mixture kinetics
**URL:** https://discourse.julialang.org/t/julia-differentialequations-for-state-to-state-binary-mixture-kinetics/50807
**Category:** General Usage
**Created:** [November 26, 2020, 10:34am UTC](https://discourse.julialang.org/t/julia-differentialequations-for-state-to-state-binary-mixture-kinetics/50807 "2020-11-26T10:34:57Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@lkampoli](https://discourse.julialang.org/u/lkampoli)
#### Post date: [November 26, 2020, 10:34am UTC](https://discourse.julialang.org/t/julia-differentialequations-for-state-to-state-binary-mixture-kinetics/50807/1 "2020-11-26T10:34:58Z")
Hello, I’m quite new to Julia and I’m considering the following problem. I’d like to solve the (possible stiff) ODE system which describes the relaxation of a flow behind a shock wave according to a state-to-state approach which means that each vibrational level of the molecular species is considered as a pseudo-species with its continuity equation. Here, I consider a binary mixture of N2/N (actually the concentration of N=0).
I have splitted the julia code in several .jl files. In the main, I call the ODE solver as follows:
```julia
prob = ODEProblem(rpart!,Y0_bar,xspan, 1.)
sol = DifferentialEquations.solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8, save_everystep=true, progress=true)
```
where Y0\_bar and xspan have been defined earlier and in the rpart.jl file I define the system:
```julia
function rpart!(du,u,p,t)
ni_b = zeros(l);
ni_b[1:l] = u[1:l]; print("ni_b = ", ni_b, "\n")
na_b = u[l+1]; print("na_b = ", na_b, "\n")
v_b = u[l+2]; print("v_b = ", v_b, "\n")
T_b = u[l+3]; print("T_b = ", T_b, "\n")
nm_b = sum(ni_b); #print("nm_b = ", nm_b, "\n")
Lmax = l-1; #println("Lmax = ", Lmax, "\n")
temp = T_b*T0; #print("T = ", temp, "\n")
ef_b = 0.5*D/T0; #println("ef_b = ", ef_b, "\n")
ei_b = e_i./(k*T0); #println("ei_b = ", ei_b, "\n")
e0_b = e_0/(k*T0); #println("e0_b = ", e0_b, "\n")
sigma = 2.; #println("sigma = ", sigma, "\n")
Theta_r = Be*h*c/k; #println("Theta_r = ", Theta_r, "\n")
Z_rot = temp./(sigma.*Theta_r); #println("Z_rot = ", Z_rot, "\n")
M = sum(m); #println("M = ", M, "\n")
mb = m/M; #println("mb = ", mb, "\n")
A = zeros(l+3,l+3)
for i = 1:l
A[i,i] = v_b
A[i,l+2] = ni_b[i]
end
A[l+1,l+1] = v_b
A[l+1,l+2] = na_b
for i = 1:l+1
A[l+2,i] = T_b
end
A[l+2,l+2] = M*v0^2/k/T0*(mb[1]*nm_b+mb[2]*na_b)*v_b
A[l+2,l+3] = nm_b+na_b
for i = 1:l
A[l+3,i] = 2.5*T_b+ei_b[i]+e0_b
end
A[l+3,l+1] = 1.5*T_b+ef_b
A[l+3,l+2] = 1/v_b*(3.5*nm_b*T_b+2.5*na_b*T_b+sum((ei_b.+e0_b).*ni_b)+ef_b*na_b)
A[l+3,l+3] = 2.5*nm_b+1.5*na_b
AA = inv(A); println("AA = ", AA, "\n", size(AA), "\n")
# Equilibrium constant for DR processes
Kdr = (m[1]*h^2/(m[2]*m[2]*2*pi*k*temp))^(3/2)*Z_rot*exp.(-e_i/(k*temp))*exp(D/temp); println("Kdr = ", Kdr, "\n")
# Dissociation processes
kd = zeros(2,l)
kd = kdis(temp) * Delta*n0/v0;
println("kd = ", kd, "\n", size(kd), "\n")
# Recombination processes
kr = zeros(2,l)
for iM = 1:2
kr[iM,:] = kd[iM,:] .* Kdr * n0
end
println("kr = ", kr, "\n", size(kr), "\n")
RD = zeros(l)
for i1 = 1:l
RD[i1] = nm_b*(na_b*na_b*kr[1,i1]-ni_b[i1]*kd[1,i1]) + na_b*(na_b*na_b*kr[2,i1]-ni_b[i1]*kd[2,i1])
end
println("RD = ", RD, "\n", size(RD))
B = zeros(l+3)
for i = 1:l
B[i] = RD[i]
end
B[l+1] = - 2*sum(RD)
du = AA*B
end
```
All constant parameters are correctly set. The problem is that when I run the simulation and plot the solution it looks like nothing happened and all profiles are equal and flat. In fact, the solution at each time-step is equal to itself. So, I think I make some mistake in the update of u and du but I cannot fix it. In the Matlab version I obtain a correct evolution.
Kind regards,
Lorenzo
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [November 26, 2020, 10:41am UTC](https://discourse.julialang.org/t/julia-differentialequations-for-state-to-state-binary-mixture-kinetics/50807/2 "2020-11-26T10:41:29Z")
`du .= AA*B`