$$dy/dt = f(t,y)$$
The Rfunction vode provides an interface to the Fortran ODE
solver of the same name, written by Peter N. Brown, Alan C. Hindmarsh
and George D. Byrne.
The system of ODE's is written as an Rfunction or be defined in
compiled code that has been dynamically loaded.
In contrast to lsoda, the user has to specify whether or
not the problem is stiff and choose the appropriate solution method.
vode is very similar to lsode, but uses a
variable-coefficient method rather than the fixed-step-interpolate
methods in lsode. In addition, in vode it is possible
to choose whether or not a copy of the Jacobian is saved for reuse in
the corrector iteration algorithm; In lsode, a copy is not
kept.
vode(y, times, func, parms, rtol = 1e-6, atol = 1e-8,
jacfunc = NULL, jactype = "fullint", mf = NULL, verbose = FALSE,
tcrit = NULL, hmin = 0, hmax = NULL, hini = 0, ynames = TRUE, maxord = NULL,
bandup = NULL, banddown = NULL, maxsteps = 5000, dllname = NULL,
initfunc = dllname, initpar = parms, rpar = NULL,
ipar = NULL, nout = 0, outnames = NULL, ...)y
has a name attribute, the names will be used to label the output
matrix.times must be the initial time; if only one step is
to be taken; set times = NULL.t, or a character string giving the name of a compiled function in a
dynamically loaded shared library.
func or
jacfunc.y. See details.y. See details.NULL, an Rfunction that computes the
jacobian of the system of differential equations dydot(i)/dy(j), or
a string giving the name of a function or subroutine in
"fullint", "fullusr", "bandusr" or
"bandint" - either full or banded and estimated internally or
by user; overruled if mf is not NULL.jactype - provides more options than jactype - see
details.NULL, then vode cannot integrate
past tcrit. The Fortran routine dvode overshoots its
targets (times points in the vector times), and interpolates
values for the desired ttimes, to avoid that the simulation possibly ignores
short-term events. If 0, no maximal size is specified.FALSE: names of state variables are not
passed to function func ; this may speed up the simulation
especially for multi-D models.func and jacfunc.
See package vignette.initfunc is in the dll: the
parameters passed to the initialiser, to initialise the common
blocks (fortran) or global variables (C, C++).func and jacfunc.func and jacfunc.dllname is specified and the model is
defined in compiled code: the number of output variables calculated
in the compiled function func, present in the shared
library. Note: it is not automatically checkenout > 0: the names of output variables calculated in the
compiled function func, present in the shared library.func and
jacfunc allowing this to be a generic function.y plus the number of "global" values
returned in the next elements 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 Fortran routine `vode'
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. See details. The first
element of istate returns the conditions under which the last call to
lsoda returned. Normal is istate[1] = 2. If verbose =
TRUE, the settings of istate and rstate will be written to the
screen.vode, the user has to decide
whether or not the problem is stiff.
If the problem is nonstiff, use method flag mf = 10, which
selects a nonstiff (Adams) method, no Jacobian used.
If the problem is stiff, there are four standard choices which can be
specified with jactype or mf.
The options for jactype are
[object Object],[object Object],[object Object],[object Object]
More options are available when specifying mf directly.
The legal values of mf are 10, 11, 12, 13, 14, 15, 20, 21, 22,
23, 24, 25, -11, -12, -14, -15, -21, -22, -24, -25.
mf is a signed two-digit integer, mf = JSV*(10*METH +
MITER), where
[object Object],[object Object],[object Object]
If MITER = 1 or 4, the user must supply a subroutine jacfunc.
The example for integrator lsode demonstrates how to
specify both a banded and full jacobian.
The input parameters rtol, and atol determine the
error control performed by the solver. If the request for
precision exceeds the capabilities of the machine, vode will return an
error code. See lsoda for details.
Models may be defined in compiled C or Fortran code, as well as
in an R-function. See package vignette for details.
The output will have the attributes istate, and rstate,
two vectors with several useful elements.
If verbose = TRUE, the settings of istate and rstate will be
written to the screen.
The following elements of istate are meaningful:
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
rstate contains the following:
[object Object],[object Object],[object Object],[object Object]
For more information, see the comments in the original code dvode.fG. D. Byrne and A. C. Hindmarsh, 1975. A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations. ACM Trans. Math. Software, 1, pp. 71-96.
A. C. Hindmarsh and G. D. Byrne, 1977. EPISODE: An Effective Package for the Integration of Systems of Ordinary Differential Equations. LLNL Report UCID-30112, Rev. 1.
G. D. Byrne and A. C. Hindmarsh, 1976. EPISODEB: An Experimental Package for the Integration of Systems of Ordinary Differential Equations with Banded Jacobians. LLNL Report UCID-30132, April 1976.
A. C. Hindmarsh, 1983. ODEPACK, a Systematized Collection of ODE
Solvers. in Scientific Computing, R. S. Stepleman et al., eds.,
North-Holland, Amsterdam, pp. 55-64.
K. R. Jackson and R. Sacks-Davis, 1980. An Alternative Implementation
of Variable Step-Size Multistep Formulas for Stiff ODEs. ACM
Trans. Math. Software, 6, pp. 295-318.
Netlib:
ode, lsoda, lsode,
lsodes, lsodar, daspk,
rk.## The famous Lorenz equations: chaos in the earth's atmosphere
## Lorenz 1963. J. Atmos. Sci. 20, 130-141.
chaos <- function(t, state, parameters)
{
with(as.list(c(state)),{
dx <- -8/3*x+y*z
dy <- -10*(y-z)
dz <- -x*y+28*y-z
list(c(dx, dy, dz))
})
}
state <- c(x = 1, y = 1, z = 1)
times <- seq(0, 100, 0.01)
out <- as.data.frame(vode(state, times, chaos, 0))
plot(out$x, out$y, type = "l", main = "Lorenz butterfly")Run the code above in your browser using DataLab