[R] Differential problem

[Berend Hasselman]

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[1]*Pt,
>           B = xi[2]*Pt,
>           C = xi[3]*Pt,
>           D = xi[4]*Pt,
>           E = xi[5]*Pt,
>           I = xi[6]*Pt,
>           G = xi[7]*Pt,
>           H = xi[8]*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)
> head(out)
> 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)
> Error in eval(expr, envir, enclos) : object 'dA' not found.
> 

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[1] + y[1] - y[2]
> + res2 <- y[2] * y[1] - 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