ex_pollution: Pollution Problem, from Chemistry, ODE

Description Usage Arguments Details Value Note Author(s) References Examples

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

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pollution (times = seq(0, 60, 1), yini = NULL, 
           parms = list(), printmescd = TRUE, method = mebdfi, 
           atol = 1e-6, rtol = 1e-6,  ...)   

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

atol

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

rtol

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

printmescd

if TRUE the mixed error significant digits computed using the reference solution at time 1e13 are printed

...

additional arguments passed to the solver .

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

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.

Note

This model is implemented in R

Author(s)

Karline Soetaert <[email protected]>

Francesca Mazzia

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

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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")))    

deTestSet documentation built on May 29, 2017, 2:56 p.m.