ode.band {deSolve} | R Documentation |
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, bandup=nspec, banddown=nspec, method="lsode",...)
y |
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:
yprime = func(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 .
|
parms |
parameters passed to func |
nspec |
the number of *species* (components) in the model. |
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" |
... |
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 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 vode returned. Normal is istate = 2.
If verbose
= TRUE, the settings of istate and rstate will be written to the screen
Karline Soetaert <k.soetaert@nioo.knaw.nl>
ode.1D
, for integrating, when the jacobian matrix is banded, and where the state variables need to be rearranged
# The Aphid model from Soetaert and Herman, 2008. # 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 # the output list(dAPHIDS ) } # end of model #==================# # 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) #==================# # Plotting output # #==================# # the data in 'out' consist of: 1st col times, 2-41: the density # select the density data DENSITY <- out[,2:(numboxes +1)] filled.contour(x=times,y=Distance,DENSITY,color= topo.colors, xlab="time, days", ylab= "Distance on plant, m", main="Aphid density on a row of plants")