steady {rootSolve} | R Documentation |
Estimates the steady-state condition for a system of ordinary differential equations.
This is a wrapper around steady-state solvers stode
, stodes
and runsteady
.
steady(y, time=0, func, parms=NULL, method="stode",...)
y |
the initial guess of (state) values for the ODE system, a vector.
If y has a name attribute, the names will be used to label the output matrix.
|
time |
time for which steady-state is wanted; the default is time=0. |
func |
either an R-function that computes the values of the
derivatives in the ode system (the model defininition) at time time ,
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 whose steady-state
value is also required.
The derivatives should be specified in the same order as the state variables y .
|
parms |
parameters passed to func .
|
method |
the solution method to use, one of stode , stodes
or runsteady .
|
... |
additional arguments passed to function stode ,
stodes or runsteady .
|
This is simply a wrapper around the various steady-state solvers.
See package vignette for information about specifying the model in compiled code.
See the selected solver for the additional options.
A list containing
y |
a vector with the state variable values from the last iteration
during estimation of steady-state condition of the system of equations.
If y has a names attribute, it will be used to label the output values. |
... |
the number of "global" values returned. |
The output will have the attribute steady
, which returns TRUE
,
if steady-state has been reached and the attribute
precis
with the precision attained during each iteration.
Karline Soetaert <k.soetaert@nioo.knaw.nl>
steady.band
, to find the steady-state of ODE models with a
banded Jacobian
steady.1D
, steady.2D
,
steady.3D
, steady-state solvers for 1-D, 2-D and 3-D
partial differential equations.
stode
, iterative steady-state solver for ODEs with full
or banded Jacobian.
stodes
, iterative steady-state solver for ODEs with arbitrary
sparse Jacobian.
runsteady
, steady-state solver by dynamically running to
steady-state
## ======================================================================= ## Bacteria (Bac) growing on a substrate (Sub) ## ======================================================================= model <- function(t,state,pars) { with (as.list(c(state,pars)), { # substrate uptake death respiration dBact = gmax*eff*Sub/(Sub+ks)*Bact - dB*Bact - rB*Bact dSub =-gmax *Sub/(Sub+ks)*Bact + dB*Bact +input return(list(c(dBact,dSub))) }) } pars <- list(gmax =0.5,eff = 0.5, ks =0.5, rB =0.01, dB =0.01, input=0.1) # Newton-Raphson steady(y=c(Bact=0.1,Sub=0),time=0, func=model,parms=pars,pos=TRUE) # Dynamic run to steady-state as.data.frame(steady(y=c(Bact=0.1,Sub=0),time=c(0,1e5), func=model,parms=pars,method="runsteady"))