# [R] Differential problem

Raphaëlle Carraud raphaelle.carraud at oc-metalchem.com
Thu Jul 11 14:19:02 CEST 2013

```Ok, now it's good (Pt was in my workplace so it worked for me, I am not used to R using these value to make the program run so I hadn't looked...)

reaction<-function(z, state, dval, parameters) {
with(as.list(c(state,dval,parameters)),{
# rate of change

Tr <- 273+90
P <- 0.98*10^5

K2 <- 10^(2993/Tr-9.226)*(10^-3)
K3 <- 10^(2072/Tr-7.234)*(10^-3)
K4 <- 10^(-20.83/Tr-0.5012)
K5 <- 10^(-965.5/Tr-1.481)
k1 <- (10^(652.1/Tr-0.7356))*(8.314*Tr/P)^2
kf2 <- 1.4*10^-33*(Tr/300)^(-3.8)*6.022*10^23*10^-6
kb2 <- kf2/K2*P/(8.314*Tr)
kf3 <- 3.1*10^-34*(Tr/300)^(-7.7)*10^(-6)*6.022*10^23
kb3 <- kf3/K3*P/(8.314*Tr)
kf4 <- 41
kf5 <- 0.25

r1 <- k1*A^2*H
r4 <- kf4*D*G - kf4/K4*E^2
r5 <- kf5*C*G - kf5/K5*E*I

res1 <- -dA + dB + 2*dC - 2*r1 - 2*r5          #
res2 <- dA + dD + r1 + r4                     #
res3 <- K2 - C/B^2                             #
res4 <- K3 - D/(A*B)                           #
res5 <- r5 + 2*r4 - dE             #dHNO2/dz
res6 <- r5 -dI                   #dHNO3/dz
res7 <- -r5 - r4 - dG             #dH2O/dz
res8 <- -r1/2 - dH                #dO2/dz

list(c(res1, res2, res3, res4, res5, res6, res7, res8))
})   # end with(as.list ...
}

xi <- c(0.3,   #x_NO
0.1,   #x_NO2
0,     #x_N2O4
0,     #x_N2O3
0.05,  #x_HNO2
0.05,  #x_HNO3
0.2,   #x_H2O
0.3)   #x_O2

Pt <- 0.98*10^5
state <- c(A = xi*Pt,
B = xi*Pt,
C = xi*Pt,
D = xi*Pt,
E = xi*Pt,
I = xi*Pt,
G = xi*Pt,
H = xi*Pt)

dval <- c(dA = 1,
dB = 1,
dC = 0.5,
dD = 0.2,
dE = 0,
dI = 0,
dG = 0,
dH = 0)

parameters <- c(Pt = 0.98*10^5)

z <- seq(0, 1, by = 0.01)  # en seconde

library(deSolve)
#out <- ode(y = state, times = z, func = reaction, parameters)

out <- daspk(y = state, dy = dval, times = z, res = reaction, parms = 0)
plot(out)

-----Message d'origine-----
De : Berend Hasselman [mailto:bhh at xs4all.nl]
Envoyé : jeudi 11 juillet 2013 14:13
À : Raphaëlle Carraud
Cc : r-help at r-project.org
Objet : Re: [R] Differential problem

On 11-07-2013, at 13:53, Raphaëlle Carraud <raphaelle.carraud at oc-metalchem.com> wrote:

> Sorry for the bug, I had eliminated some lines to avoid making the program too big. Here is the version that works :
>
> reaction<-function(z, state, dval, parameters) {
> with(as.list(c(state)),{
>    # rate of change
>
>    Tr <- 273+90
>    P <- 0.98*10^5
>
>    K2 <- 10^(2993/Tr-9.226)*(10^-3)
>    K3 <- 10^(2072/Tr-7.234)*(10^-3)
>    K4 <- 10^(-20.83/Tr-0.5012)
>    K5 <- 10^(-965.5/Tr-1.481)
>    k1 <- (10^(652.1/Tr-0.7356))*(8.314*Tr/P)^2
>    kf2 <- 1.4*10^-33*(Tr/300)^(-3.8)*6.022*10^23*10^-6
>    kb2 <- kf2/K2*P/(8.314*Tr)
>    kf3 <- 3.1*10^-34*(Tr/300)^(-7.7)*10^(-6)*6.022*10^23
>    kb3 <- kf3/K3*P/(8.314*Tr)
>    kf4 <- 41
>    kf5 <- 0.25
>
>    r1 <- k1*A^2*H
>    r4 <- kf4*D*G - kf4/K4*E^2
>    r5 <- kf5*C*G - kf5/K5*E*I
>
>    res1 <- -dA + dB + 2*dC - 2*r1 - 2*r5          #
>    res2 <- dA + dD + r1 + r4                     #
>    res3 <- K2 - C/B^2                             #
>    res4 <- K3 - D/(A*B)                           #
>    res5 <- r5 + 2*r4 - dE             #dHNO2/dz
>    res6 <- r5 -dI                   #dHNO3/dz
>    res7 <- -r5 - r4 - dG             #dH2O/dz
>    res8 <- -r1/2 - dH                #dO2/dz
>
>    list(c(res1, res2, res3, res4, res5, res6, res7, res8))
>  })   # end with(as.list ...
> }
>
> xi <- c(0.3,   #x_NO
>        0.1,   #x_NO2
>        0,     #x_N2O4
>        0,     #x_N2O3
>        0.05,  #x_HNO2
>        0.05,  #x_HNO3
>        0.2,   #x_H2O
>        0.3)   #x_O2
>
>
> state <- c(A = xi*Pt,
>           B = xi*Pt,
>           C = xi*Pt,
>           D = xi*Pt,
>           E = xi*Pt,
>           I = xi*Pt,
>           G = xi*Pt,
>           H = xi*Pt)
>
> dval <- c(dA = 1,
>          dB = 1,
>          dC = 0.5,
>          dD = 0.2,
>          dE = 0,
>          dI = 0,
>          dG = 0,
>          dH = 0)
>
> parameters <- c(Pt = 0.98*10^5)
>

Doesn't run.
Since variable Pt is not defined when you calculate vector state. So define Pt <- .. before xi as in the original example.

In the function reaction isn't variable P just Pt from the parameter vector?
If so then either do P <- Pt or just use Pt directly (but see next remark).

> z <- seq(0, 1, by = 0.01)  # en seconde
>
> library(deSolve)
> #out <- ode(y = state, times = z, func = reaction, parameters)
>
> out <- daspk(y = state, dy = dval, times = z, res = reaction, parms =
> 0)
> plot(out)
>
> I obtain the following message:
>
>> library(deSolve)
>> #out <- ode(y = state, times = z, func = reaction, parameters)
>>
>> out <- daspk(y = state, dy = dval, times = z, res = reaction, parms =
>> 0)
>

Obviously since dA  isn't defined outside of dval when the functions was defined.
And do parms=parameters if you want to use Pt (as I told you in the previous post).

> I tried adding the dval and parameters as you said:
> with(as.list(c(state,dval,parameters)),{
>
> I get the following message:
>
> Warning messages:
> 1: In daspk(y = state, dy = dval, times = z, res = reaction, parms = 0) :
>  matrix of partial derivatives is singular with direct method-some
> equations redundant
> 2: In daspk(y = state, dy = dval, times = z, res = reaction, parms = 0) :
>  Returning early. Results are accurate, as far as they go
>

These are warning messages.
You get plots.
So now is the time to start looking at initial values etc.

Since I know next to nothing about DAE's you are on your own here unless someone else comes up with suggestions.

> For the calling of the daspk function, I followed the documentation, where you have the same inversion:
>
> daefun <- function(t, y, dy, parameters) {
> + res1 <- dy + y - y
> + res2 <- y * y - t
> +
> + list(c(res1, res2))
> + }
>> library(deSolve)
>> yini <- c(1, 0)
>> dyini <- c(1, 0)
>> times <- seq(0, 10, 0.1)
>> ## solver
>> system.time(out <- daspk(y = yini, dy = dyini, times = times, res =
>> daefun, parms = 0))
>
> Is it wrong? When I modify the order, I obtain again that object dA is not found, so I guessed the doc was right.
>

Of course see above.

Berend

```