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].
hires (yini = NULL, times = seq(0, 321.8122, by = 321.8122/500),
parms = list(), printmescd = TRUE, method = mebdfi,
atol = 1e-6, rtol = 1e-6, ...)
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.
the initial (state) values for the DE system. If y
has a name attribute, the names will be used to label the output
matrix.
time sequence for which output is wanted; the first
value of times
must be the initial time.
absolute error tolerance, either a scalar or a vector, one value for each y.
relative error tolerance, either a scalar or a vector, one value for each y,
the solver to use
list of parameters that overrule the default parameter values
if TRUE the mixed error significant digits computed using the reference solution at time 321.8122 are printed
additional arguments passed to the solver .
Karline Soetaert <karline.soetaert@nioz.nl>
Francesca Mazzia <mazzia@dm.uniba.it>
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
url : archimede.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.
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")))
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