ode.3D {deSolve}  R Documentation 
Solver for 3Dimensional Ordinary Differential Equations
Description
Solves a system of ordinary differential equations resulting from 3Dimensional partial differential equations that have been converted to ODEs by numerical differencing.
Usage
ode.3D(y, times, func, parms, nspec = NULL, dimens,
method = c("lsodes", "euler", "rk4", "ode23", "ode45", "adams", "iteration"),
names = NULL, cyclicBnd = 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
If The return value of 
parms 
parameters passed to 
nspec 
the number of species (components) in the model. 
dimens 
3valued vector with the number of boxes in three dimensions in the model. 
names 
the names of the components; used for plotting. 
cyclicBnd 
if not 
method 
the integrator. Use Method 
... 
additional arguments passed to 
Details
This is the method of choice for 3dimensional models, that are only subjected to transport between adjacent layers.
Based on the dimension of the problem, the method first calculates the
sparsity pattern of the Jacobian, under the assumption that transport
is only occurring between adjacent layers. Then lsodes
is
called to solve the problem.
As lsodes
is used to integrate, it will probably be necessary
to specify the length of the real work array, lrw
.
Although a reasonable guess of lrw
is made, it is likely that
this will be too low.
In this case, ode.2D
will return with an
error message telling the size of the work array actually needed. In
the second try then, set lrw
equal to this number.
For instance, if you get the error:
DLSODES RWORK length is insufficient to proceed. Length needed is .ge. LENRW (=I1), exceeds LRW (=I2) In above message, I1 = 27627 I2 = 25932
set lrw
equal to 27627 or a higher value.
See lsodes 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 useful elements. 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. See the
help for the selected integrator for details.
Note
It is advisable though not mandatory to specify both
nspec
and dimens
. In this case, the solver can check
whether the input makes sense (as nspec*dimens[1]*dimens[2]*dimens[3]
== length(y)
).
Do not use this method for problems that are not 3D!
Author(s)
Karline Soetaert <karline.soetaert@nioz.nl>
See Also

ode
for a general interface to most of the ODE solvers, 
ode.band
for integrating models with a banded Jacobian 
ode.1D
for integrating 1D models 
ode.2D
for integrating 2D models 
lsodes
for the integration options.
diagnostics
to print diagnostic messages.
Examples
## =======================================================================
## Diffusion in 3D; imposed boundary conditions
## =======================================================================
diffusion3D < function(t, Y, par) {
## function to bind two matrices to an array
mbind < function (Mat1, Array, Mat2, along = 1) {
dimens < dim(Array) + c(0, 0, 2)
if (along == 3)
array(dim = dimens, data = c(Mat1, Array, Mat2))
else if (along == 1)
aperm(array(dim = dimens,
data=c(Mat1, aperm(Array, c(3, 2, 1)), Mat2)), c(3, 2, 1))
else if (along == 2)
aperm(array(dim = dimens,
data = c(Mat1, aperm(Array, c(1, 3, 2)), Mat2)), c(1, 3, 2))
}
yy < array(dim=c(n, n, n), data = Y) # vector to 3D array
dY < r*yy # consumption
BND < matrix(nrow = n, ncol = n, data = 1) # boundary concentration
## diffusion in xdirection
## new array including boundary concentrations in Xdirection
BNDx < mbind(BND, yy, BND, along = 1)
## diffusive Flux
Flux < Dx * (BNDx[2:(n+2),,]  BNDx[1:(n+1),,])/dx
## rate of change =  flux gradient
dY[] < dY[]  (Flux[2:(n+1),,]  Flux[1:n,,])/dx
## diffusion in ydirection
BNDy < mbind(BND, yy, BND, along = 2)
Flux < Dy * (BNDy[,2:(n+2),]  BNDy[,1:(n+1),])/dy
dY[] < dY[]  (Flux[,2:(n+1),]  Flux[,1:n,])/dy
## diffusion in zdirection
BNDz < mbind(BND, yy, BND, along = 3)
Flux < Dz * (BNDz[,,2:(n+2)]  BNDz[,,1:(n+1)])/dz
dY[] < dY[]  (Flux[,,2:(n+1)]  Flux[,,1:n])/dz
return(list(as.vector(dY)))
}
## parameters
dy < dx < dz <1 # grid size
Dy < Dx < Dz <1 # diffusion coeff, X and Ydirection
r < 0.025 # consumption rate
n < 10
y < array(dim=c(n,n,n),data=10.)
## use lsodes, the default (for n>20, RungeKutta more efficient)
print(system.time(
RES < ode.3D(y, func = diffusion3D, parms = NULL, dimens = c(n, n, n),
times = 1:20, lrw = 120000, atol = 1e10,
rtol = 1e10, verbose = TRUE)
))
y < array(dim = c(n, n, n), data = RES[nrow(RES), 1])
filled.contour(y[, , n/2], color.palette = terrain.colors)
summary(RES)
## Not run:
for (i in 2:nrow(RES)) {
y < array(dim=c(n,n,n),data=RES[i,1])
filled.contour(y[,,n/2],main=i,color.palette=terrain.colors)
}
## End(Not run)