deTestSet (version 1.0)

hires: High Irradiance Response model, from Plant Physiology, ODE

Description

This IVP is a stiff system of 8 non-linear Ordinary Differential Equations.

It was proposed by Schafer in 1975 [Sch75].

The name HIRES was given by Hairer & Wanner [HW96]. It refers to 'High Irradiance RESponse', which is described by this ODE.

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

Usage

hires (times = seq(0, 5, by = 0.01), yini = NULL, parms = list(),  ...)

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

...

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 = 1.71, k2 = 0.43, k3 = 8.32, k4 = 0.69, k5 = 0.035, k6 = 8.32, k7 = 280, k8 = 0.69, k9 = 0.69, Oks = 0.0007

References

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

[Got77] B.A. Gottwald. MISS - ein einfaches Simulations-System fur biologische und chemische Prozesse. EDV in Medizin und Biologie, 3:85-90, 1977.

[HW96] E. Hairer and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential- algebraic Problems. Springer-Verlag, second revised edition, 1996.

[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. Available at http://www.dm.uniba.it/testset.

[Sch75] E. Schafer. A new approach to explain the 'high irradiance responses' of photomorphogenesis on the basis of phytochrome. J. of Math. Biology, 2:41 - 56, 1975.

[SL98] J.J.B. de Swart and W.M. Lioen. Collecting real-life problems to test solvers for implicit differential equations. CWI Quarterly, 11(1):83 - 100, 1998.

Examples

out <- hires()
plot(out, lwd = 2)

# compare with reference solution
out1 <- hires(times = c(0, 321.8122))

max(abs(out1[nrow(out1),-1] - reference("hires")))