R: Solver for Ordinary Differential Equations; Assumes a Banded...
ode.band
R Documentation
Solver for Ordinary Differential Equations; Assumes a Banded
Jacobian
Description
Solves a system of ordinary differential equations.
Assumes a banded Jacobian matrix, but does not rearrange the state
variables (in contrast to ode.1D). Suitable for 1-D models that
include transport only between adjacent layers and that model only one
species.
the initial (state) values for the ODE system, a vector. 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.
func
either an R-function that computes the values of the
derivatives in the ODE system (the model definition) at time
t, or a character string giving the name of a compiled
function in a dynamically loaded shared library.
If func is an R-function, it must be defined as:
func <- function(t, y, parms, ...). t is the current time
point in the integration, y is the current estimate of the
variables in the ODE system. If the initial values y has a
names attribute, the names will be available inside func.
parms is a vector or list of parameters; ... (optional) are
any other arguments passed to the function.
The return value of func should be a list, whose first
element is a vector containing the derivatives of y with
respect to time, and whose next elements are global values
that are required at each point in times.The derivatives
must be specified in the same order as the state variables y.
parms
parameters passed to func.
nspec
the number of *species* (components) in the model.
dimens
the number of boxes in the model. If NULL, then
nspec should be specified.
bandup
the number of nonzero bands above the Jacobian
diagonal.
banddown
the number of nonzero bands below the Jacobian
diagonal.
method
the integrator to use, one of "vode",
"lsode", "lsoda", "lsodar", "radau".
names
the names of the components; used for plotting.
...
additional arguments passed to the integrator.
Details
This is the method of choice for single-species 1-D reactive transport
models.
For multi-species 1-D models, this method can only be used if the
state variables are arranged per box, per species (e.g. A[1], B[1],
A[2], B[2], A[3], B[3], ... for species A, B). By default, the
model function will have the species arranged as A[1], A[2],
A[3], ... B[1], B[2], B[3], ... in this case, use ode.1D.
See the selected integrator for the additional options.
Value
A matrix of class deSolve with up to as many rows as elements in times and as
many columns as elements in y plus the number of "global"
values returned in the second element of the return from func,
plus an additional column (the first) for the time value. There will
be one row for each element in times unless the integrator
returns with an unrecoverable error. If y has a names
attribute, it will be used to label the columns of the output value.
The output will have the attributes istate and rstate,
two vectors with several elements. See the help for the selected
integrator for details. the first element of istate returns the
conditions under which the last call to the integrator returned. Normal is
istate = 2. If verbose = TRUE, the settings of
istate and rstate will be written to the screen.
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>
See Also
ode for a general interface to most of the ODE solvers,
ode.1D for integrating 1-D models
ode.2D for integrating 2-D models
ode.3D for integrating 3-D models
lsode, lsoda, lsodar,
vode for the integration options.
diagnostics to print diagnostic messages.
Examples
## =======================================================================
## The Aphid model from Soetaert and Herman, 2009.
## A practical guide to ecological modelling.
## Using R as a simulation platform. Springer.
## =======================================================================
## 1-D diffusion model
## ================
## Model equations
## ================
Aphid <- function(t, APHIDS, parameters) {
deltax <- c (0.5, rep(1, numboxes-1), 0.5)
Flux <- -D*diff(c(0, APHIDS, 0))/deltax
dAPHIDS <- -diff(Flux)/delx + APHIDS*r
list(dAPHIDS) # the output
}
## ==================
## Model application
## ==================
## the model parameters:
D <- 0.3 # m2/day diffusion rate
r <- 0.01 # /day net growth rate
delx <- 1 # m thickness of boxes
numboxes <- 60
## distance of boxes on plant, m, 1 m intervals
Distance <- seq(from = 0.5, by = delx, length.out = numboxes)
## Initial conditions, ind/m2
## aphids present only on two central boxes
APHIDS <- rep(0, times = numboxes)
APHIDS[30:31] <- 1
state <- c(APHIDS = APHIDS) # initialise state variables
## RUNNING the model:
times <- seq(0, 200, by = 1) # output wanted at these time intervals
out <- ode.band(state, times, Aphid, parms = 0,
nspec = 1, names = "Aphid")
## ================
## Plotting output
## ================
image(out, grid = Distance, method = "filled.contour",
xlab = "time, days", ylab = "Distance on plant, m",
main = "Aphid density on a row of plants")
matplot.1D(out, grid = Distance, type = "l",
subset = time %in% seq(0, 200, by = 10))
# add an observed dataset to 1-D plot (make sure to use correct name):
data <- cbind(dist = c(0,10, 20, 30, 40, 50, 60),
Aphid = c(0,0.1,0.25,0.5,0.25,0.1,0))
matplot.1D(out, grid = Distance, type = "l",
subset = time %in% seq(0, 200, by = 10),
obs = data, obspar = list(pch = 18, cex = 2, col="red"))
## Not run:
plot.1D(out, grid = Distance, type = "l")
## End(Not run)