deTestSet (version 1.0)

emep: Emep MSC-W Ozone Chemistry Problem, ODE

Description

The problem is a stiff system of 66 ordinary differential equations. The 'Mathematics and the Environment' project group at CWI contributed this problem to the test set. The software part of the problem is in the file emep.f available at [MM08].

Usage

emep (times = seq(14400, 417600, by = 400), yini = NULL, 
  parms = list(), rtol = 1e-5, atol = 0.1, maxsteps = 1e5, ...)

Arguments

yini

the initial (state) values for the DE system. If y has a name attribute, the names will be used to label the output matrix.

times

time sequence for which output is wanted; the first value of times must be the initial time.

parms

list of parameters that overrule the default parameter values

rtol

relative error tolerance, either a scalar or a vector, one value for each y,

atol

absolute error tolerance, either a scalar or a vector, one value for each y.

maxsteps

maximal number of steps per output interval taken by the solver

...

additional arguments passed to the solver .

Value

• A matrix of class deSolve with up to as many rows as elements in times and as many columns as elements in yini, plus an additional column (the first) for the time value.

  There will be one row for each element in times unless the solver returns with an unrecoverable error. If yini has a names attribute, it will be used to label the columns of the output value.

Details

The default parameters are:

c = 1.6e-8 , cs = 2e-12 , cp = 1e-8 , r = 25e3 , rp = 50, lh = 4.45 , ls1 = 2e-3 , ls2 = 5e-4 , ls3 = 5e-4, rg1 = 36.3 , rg2 = 17.3 , rg3 = 17.3 , ri = 50 , rc = 600, gamma = 40.67286402e-9 , delta = 17.7493332

References

http://www.dm.uniba.it/~testset

[MM08] F. Mazzia and C. Magherini. Test Set for Initial Value Problem Solvers, release 2.4. Department of Mathematics, University of Bari and INdAM, Research Unit of Bari, February 2008.

[SASJ93] D. Simpson, Y. Andersson-Skold, and M.E. Jenkin. Updating the chemical scheme for the EMEP MSC-W model: Current status. Report EMEP MSC-W Note 2/93, The Norwegian Meteorological Institute, Oslo, 1993.

[Sim93] D. Simpson. Photochemical model calculations over Europe for two extended summer periods: 1985 and 1989. model results and comparisons with observations. Atmospheric Environment, 27A:921-943, 1993.

[VS94] J.G. Verwer and D. Simpson. Explicit methods for stiff ODEs from atmospheric chemistry. Report NM-R9409, CWI, Amsterdam, 1994.

Examples

out <- emep()
plot(out, lwd = 2, col = "darkblue", 
  which = c("NO", "NO2", "SO2", "CH4", "O3", "N2O5"))

plot(out, col = "darkblue", lwd = 2, which = 1:16)
mtext(side = 3,line = -1.5, "emep", cex = 1.25, outer = TRUE)

# compare with reference solution (component 36 adn 38 not included)       
refsol <- reference("emep")
inderr <- c(1:35,37,39:66)
max(abs(out[nrow(out),inderr+1] - refsol[inderr])/refsol[inderr])