Solver for Ordinary Differential Equations; Assumes a Banded Jacobian
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.
ode.band(y, times, func, parms, nspec = NULL, dimens = NULL, bandup = nspec, banddown = nspec, method = "lsode", names = NULL, ...)
y |
the initial (state) values for the ODE system, a vector. If
|
times |
time sequence for which output is wanted; the first
value of |
func |
either an R-function that computes the values of the
derivatives in the ODE system (the model definition) at time
If The return value of |
parms |
parameters passed to |
nspec |
the number of *species* (components) in the model. |
dimens |
the number of boxes in the model. If |
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 |
names |
the names of the components; used for plotting. |
... |
additional arguments passed to the integrator. |
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.
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.
Karline Soetaert <karline.soetaert@nioz.nl>
diagnostics to print diagnostic messages.
## =======================================================================
## 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*delx, rep(delx, numboxes-1), 0.5*delx)
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")
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