ode {deSolve}  R Documentation 
General Solver for Ordinary Differential Equations
Description
Solves a system of ordinary differential equations; a wrapper around the implemented ODE solvers
Usage
ode(y, times, func, parms,
method = c("lsoda", "lsode", "lsodes", "lsodar", "vode", "daspk",
"euler", "rk4", "ode23", "ode45", "radau",
"bdf", "bdf_d", "adams", "impAdams", "impAdams_d", "iteration"), ...)
## S3 method for class 'deSolve'
print(x, ...)
## S3 method for class 'deSolve'
summary(object, select = NULL, which = select,
subset = NULL, ...)
Arguments
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 Rfunction 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 The return value of If 
parms 
parameters passed to 
method 
the integrator to use, either a function that performs
integration, or a list of class Method 
x 
an object of class 
object 
an object of class 
which 
the name(s) or the index to the variables whose summary should be estimated. Default = all variables. 
select 
which variable/columns to be selected. 
subset 
logical expression indicating elements or rows to keep when
calculating a 
... 
additional arguments passed to the integrator or to the methods. 
Details
This is simply a wrapper around the various ode solvers.
See package vignette for information about specifying the model in compiled code.
See the selected integrator for the additional options.
The default integrator used is lsoda
.
The option method = "bdf"
provdes a handle to the backward
differentiation formula (it is equal to using method = "lsode"
).
It is best suited to solve stiff (systems of) equations.
The option method = "bdf_d"
selects the backward
differentiation formula that uses JacobiNewton iteration (neglecting the
offdiagonal elements of the Jacobian (it is equal to using
method = "lsode", mf = 23
).
It is best suited to solve stiff (systems of) equations.
method = "adams"
triggers the Adams method that uses functional
iteration (no Jacobian used);
(equal to method = "lsode", mf = 10
. It is often the best
choice for solving nonstiff (systems of) equations. Note: when functional
iteration is used, the method is often said to be explicit, although it is
in fact implicit.
method = "impAdams"
selects the implicit Adams method that uses Newton
Raphson iteration (equal to method = "lsode", mf = 12
.
method = "impAdams_d"
selects the implicit Adams method that uses Jacobi
Newton iteration, i.e. neglecting all offdiagonal elements (equal to
method = "lsode", mf = 13
.
For very stiff systems, method = "daspk"
may outperform
method = "bdf"
.
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.
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>
See Also

plot.deSolve
for plotting the outputs, 
dede
general solver for delay differential equations 
ode.band
for solving models with a banded Jacobian, 
ode.1D
for integrating 1D models, 
ode.2D
for integrating 2D models, 
ode.3D
for integrating 3D models, 
diagnostics
to print diagnostic messages.
Examples
## =======================================================================
## Example1: PredatorPrey LotkaVolterra model (with logistic prey)
## =======================================================================
LVmod < function(Time, State, Pars) {
with(as.list(c(State, Pars)), {
Ingestion < rIng * Prey * Predator
GrowthPrey < rGrow * Prey * (1  Prey/K)
MortPredator < rMort * Predator
dPrey < GrowthPrey  Ingestion
dPredator < Ingestion * assEff  MortPredator
return(list(c(dPrey, dPredator)))
})
}
pars < c(rIng = 0.2, # /day, rate of ingestion
rGrow = 1.0, # /day, growth rate of prey
rMort = 0.2 , # /day, mortality rate of predator
assEff = 0.5, # , assimilation efficiency
K = 10) # mmol/m3, carrying capacity
yini < c(Prey = 1, Predator = 2)
times < seq(0, 200, by = 1)
out < ode(yini, times, LVmod, pars)
summary(out)
## Default plot method
plot(out)
## User specified plotting
matplot(out[ , 1], out[ , 2:3], type = "l", xlab = "time", ylab = "Conc",
main = "LotkaVolterra", lwd = 2)
legend("topright", c("prey", "predator"), col = 1:2, lty = 1:2)
## =======================================================================
## Example2: SubstrateProducerConsumer LotkaVolterra model
## =======================================================================
## Note:
## Function sigimp passed as an argument (input) to model
## (see also lsoda and rk examples)
SPCmod < function(t, x, parms, input) {
with(as.list(c(parms, x)), {
import < input(t)
dS < import  b*S*P + g*C # substrate
dP < c*S*P  d*C*P # producer
dC < e*P*C  f*C # consumer
res < c(dS, dP, dC)
list(res)
})
}
## The parameters
parms < c(b = 0.001, c = 0.1, d = 0.1, e = 0.1, f = 0.1, g = 0.0)
## vector of timesteps
times < seq(0, 200, length = 101)
## external signal with rectangle impulse
signal < data.frame(times = times,
import = rep(0, length(times)))
signal$import[signal$times >= 10 & signal$times <= 11] < 0.2
sigimp < approxfun(signal$times, signal$import, rule = 2)
## Start values for steady state
xstart < c(S = 1, P = 1, C = 1)
## Solve model
out < ode(y = xstart, times = times,
func = SPCmod, parms = parms, input = sigimp)
## Default plot method
plot(out)
## User specified plotting
mf < par(mfrow = c(1, 2))
matplot(out[,1], out[,2:4], type = "l", xlab = "time", ylab = "state")
legend("topright", col = 1:3, lty = 1:3, legend = c("S", "P", "C"))
plot(out[,"P"], out[,"C"], type = "l", lwd = 2, xlab = "producer",
ylab = "consumer")
par(mfrow = mf)
## =======================================================================
## Example3: Discrete time model  using method = "iteration"
## The hostparasitoid model from Soetaert and Herman, 2009,
## Springer  p. 284.
## =======================================================================
Parasite < function(t, y, ks) {
P < y[1]
H < y[2]
f < A * P / (ks + H)
Pnew < H * (1  exp(f))
Hnew < H * exp(rH * (1  H)  f)
list (c(Pnew, Hnew))
}
rH < 2.82 # rate of increase
A < 100 # attack rate
ks < 15 # halfsaturation density
out < ode(func = Parasite, y = c(P = 0.5, H = 0.5), times = 0:50, parms = ks,
method = "iteration")
out2< ode(func = Parasite, y = c(P = 0.5, H = 0.5), times = 0:50, parms = 25,
method = "iteration")
out3< ode(func = Parasite, y = c(P = 0.5, H = 0.5), times = 0:50, parms = 35,
method = "iteration")
## Plot all 3 scenarios in one figure
plot(out, out2, out3, lty = 1, lwd = 2)
## Same like "out", but *output* every two steps
## hini = 1 ensures that the same *internal* timestep of 1 is used
outb < ode(func = Parasite, y = c(P = 0.5, H = 0.5),
times = seq(0, 50, 2), hini = 1, parms = ks,
method = "iteration")
plot(out, outb, type = c("l", "p"))
## Not run:
## =======================================================================
## Example4: Playing with the Jacobian options  see e.g. lsoda help page
##
## IMPORTANT: The following example is temporarily broken because of
## incompatibility with R 3.0 on some systems.
## A fix is on the way.
## =======================================================================
## a stiff equation, exponential decay, run 500 times
stiff < function(t, y, p) { # y and r are a 500valued vector
list( r * y)
}
N < 500
r < runif(N, 15, 20)
yini < runif(N, 1, 40)
times < 0:10
## Using the default
print(system.time(
out < ode(y = yini, parms = NULL, times = times, func = stiff)
))
# diagnostics(out) shows that the method used = bdf (2), so it it stiff
## Specify that the Jacobian is banded, with nonzero values on the
## diagonal, i.e. the bandwidth up and down = 0
print(system.time(
out2 < ode(y = yini, parms = NULL, times = times, func = stiff,
jactype = "bandint", bandup = 0, banddown = 0)
))
## Now we also specify the Jacobian function
jacob < function(t, y, p) r
print(system.time(
out3 < ode(y = yini, parms = NULL, times = times, func = stiff,
jacfunc = jacob, jactype = "bandusr",
bandup = 0, banddown = 0)
))
## The larger the value of N, the larger the time gain...
## End(Not run)