Description Usage Arguments Details Value Author(s) References See Also Examples
Solves the initial value problem for systems of ordinary differential equations (ODE) in the form:
dy/dt = f(t,y)
The R function dopri5
provides an interface to the Fortran ODE
solver DOPRI5, written by E. Hairer and G. Wanner.
It implements the explicit RungeKutta method of order 4(5) due to Dormand & Prince with stepsize control and dense output
The R function cashkarp
provides an interface to the Fortran ODE
solver CASHCARP, written by J. Cash and F. Mazzia.
It implements the explicit RungeKutta method of order 4(5) due to CashCarp, with stepsize control and dense output
The system of ODE's is written as an R function or can be defined in compiled code that has been dynamically loaded.
1 2 3 4 5 6 7 8 9 10 11  dopri5 (y, times, func, parms, rtol = 1e6, atol = 1e6,
verbose = FALSE, hmax = NULL, hini = hmax, ynames = TRUE,
maxsteps = 10000, dllname = NULL, initfunc = dllname,
initpar=parms, rpar = NULL, ipar = NULL, nout = 0,
outnames = NULL, forcings = NULL, initforc = NULL, fcontrol = NULL, ...)
cashkarp (y, times, func, parms, rtol = 1e6, atol = 1e6,
verbose = FALSE, hmax = NULL, hini = hmax, ynames = TRUE,
maxsteps = 10000, dllname = NULL, initfunc = dllname, initpar = parms,
rpar = NULL, ipar = NULL, nout = 0, outnames = NULL, forcings = NULL,
initforc = NULL, fcontrol = NULL, stiffness = 2, ...)

y 
the initial (state) values for the ODE system. 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 
vector or list of parameters used in 
rtol 
relative error tolerance, either a
scalar or an array as long as 
atol 
absolute error tolerance, either a scalar or an array as
long as 
verbose 
if 
hmax 
an optional maximum value of the integration stepsize. If
not specified, 
hini 
initial step size to be attempted. 
ynames 
logical, if 
maxsteps 
maximal number of steps taken by the solver, for the entire integration. This is different from the settings of this argument in the solvers from package deSolve! 
dllname 
a string giving the name of the shared library
(without extension) that contains all the compiled function or
subroutine definitions refered to in 
initfunc 
if not 
initpar 
only when ‘dllname’ is specified and an
initialisation function 
rpar 
only when ‘dllname’ is specified: a vector with
double precision values passed to the dllfunctions whose names are
specified by 
ipar 
only when ‘dllname’ is specified: a vector with
integer values passed to the dllfunctions whose names are specified
by 
nout 
only used if 
outnames 
only used if ‘dllname’ is specified and

forcings 
only used if ‘dllname’ is specified: a list with
the forcing function data sets, each present as a twocolumned matrix,
with (time,value); interpolation outside the interval
[min( See forcings or package vignette 
initforc 
if not 
fcontrol 
A list of control parameters for the forcing functions.
See forcings or vignette 
stiffness 
How the stiffness of the solution should be estimated.
Default = stiffness based on eigenvalue approximation;
when = 
... 
additional arguments passed to 
The work is done by the FORTRAN subroutine dop853
, whose
documentation should be consulted for details. The implementation
is based on the Fortran 77 version fromOctober 11, 2009.
The input parameters rtol
, and atol
determine the
error control performed by the solver, which roughly keeps the
local error of y(i) below rtol(i)*abs(y(i))+atol(i).
The diagnostics of the integration can be printed to screen
by calling diagnostics
. If verbose
= TRUE
,
the diagnostics will written to the screen at the end of the integration.
See vignette("deSolve") from the deSolve
package for an
explanation of each element in the vectors
containing the diagnostic properties and how to directly access them.
Models may be defined in compiled C or FORTRAN code, as well as
in an Rfunction. See package vignette "compiledCode"
from package
deSolve
for details.
Information about linking forcing functions to compiled code is in
forcings (from package deSolve
).
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 next elements of the return from func
,
plus and additional column for the time value. There will be a row
for each element in times
unless the FORTRAN routine ‘lsoda’
returns with an unrecoverable error. If y
has a names
attribute, it will be used to label the columns of the output value.
Karline Soetaert <[email protected]>
E. Hairer, S.P. Norsett AND G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series In Computational Mathematics, SPRINGERVERLAG (1993)
ode
for a general interface to most of the ODE solvers
from package deSolve
,
ode.1D
for integrating 1D models,
ode.2D
for integrating 2D models,
ode.3D
for integrating 3D models,
mebdfi
for integrating DAE models,
bimd
for blended implicit methods,
gamd
for the generalised adams method
diagnostics
to print diagnostic messages.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  ## =======================================================================
## Example :
## The Arenstorff orbit model
## =======================================================================
Arenstorff < function(t, y, parms) {
D1 < ((y[1]+mu)^2+y[2]^2)^(3/2)
D2 < ((y[1](1mu))^2+y[2]^2)^(3/2)
dy1 < y[3]
dy2 < y[4]
dy3 < y[1] + 2*y[4](1mu)*(y[1]+mu)/D1 mu*(y[1](1mu))/D2
dy4 < y[2]  2*y[3](1mu)*y[2]/D1  mu*y[2]/D2
list(c(dy1,dy2,dy3,dy4))
}
#
# parameters, initial values and times
#
mu < 0.012277471
yini < c(x = 0.994, y = 0, dx = 0,
dy = 2.00158510637908252240537862224)
times < seq(0, 18, 0.01)
#
# solve the model
#
#out < dopri5 (times=times, y=yini, func = Arenstorff, parms=NULL )
out < cashkarp (times = times, y = yini, func = Arenstorff, parms = NULL )
plot(out[,c("x", "y")], type = "l", lwd = 2, main = "Arenstorff")
#
# First and last value should be the same
#
times < c(0, 17.0652165601579625588917206249)
Test < dopri5 (times = times, y = yini, func = Arenstorff, parms = NULL)
diagnostics(Test)

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