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

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

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

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hires (yini = NULL, times = seq(0, 321.8122, by = 321.8122/500), 
       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.

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,

method

the solver to use

parms

list of parameters that overrule the default parameter values

printmescd

if TRUE the mixed error significant digits computed using the reference solution at time 321.8122 are printed

...

additional arguments passed to the solver .

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

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 <[email protected]>

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

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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")))

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