deTestSet (version 1.0)

pollution: Pollution Problem, from Chemistry, ODE

Description

This IVP is a stiff system of 20 non-linear Ordinary Differential Equations.

It is the chemical reaction part of the air pollution model developed at The Dutch National Institute of Public Health and Environmental Protection (RIVM) and it is described by Verwer in [Ver94].

The parallel-IVP-algorithm group of CWI contributed this problem to the test set. The software part of the problem is in the file pollu.f available at [MM08].

Usage

pollution (times = seq(0, 10, 0.1), yini = NULL, parms = list(), method = mebdfi,  ...)

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

method

the solver to use

...

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: k1 = .35, k2 = .266e2, k3 = .123e5, k4 = .86e-3, k5 = .82e-3, k6 = .15e5, k7 = .13e-3, k8 = .24e5,k9 = .165e5, k10 = .9e4, k11 = .22e-1, k12 = .12e5, k13 = .188e1, k14 = .163e5, k15 = .48e7, k16 = .35e-3, k17 = .175e-1, k18 = .1e9, k19 = .444e12, k20 = .124e4, k21 = .21e1, k22 = .578e1, k23 = .474e-1, k24 = .178e4, k25 = .312e1

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.

[Ver94] J.G. Verwer. Gauss-Seidel iteration for stiff ODEs from chemical kinetics. SIAM J. Sci.bComput., 15(5):1243 -- 1259,

Examples

out <- pollution()
plot(out, lwd = 2, which = 1:9)

out1 <- pollution(times = 0:60)

# compare with reference solution
max(abs(out1[nrow(out1),-1] -  reference("pollution")))