Description Usage Arguments Details Value Examples
A formula interface to integration of an ODE with respect to "t"
1  integrateODE(dyn, ..., tdur)

dyn 
a formula specifying the dynamics, e.g. 
tdur 
the duration of integration. Or, a list of the form

... 
arguments giving additional formulas for dynamics in other variables, assignments of parameters, and assignments of initial conditions 
The equations must be in firstorder form. Each dynamical equation uses
a formula interface with the variable name given on the lefthand side of the
formula, preceded by a d
, so use dx~k*x
for exponential decay.
All parameters (such as k
) must be assigned numerical values in the
argument list. All dynamical variables must be assigned initial conditions in the
argument list. The returned value will be a list with one component named after each
dynamical variable. The component will be a splinegenerated function of t
.
a list with splined function of time for each dynamical variable
1 2 3 4 5 6 7 8  soln = integrateODE(dx~r*x*(1x/k), k=10, r=.5, tdur=20, x=1)
soln$x(10)
soln$x(30) # outside the time interval for integration
# plotFun(soln$x(t)~t, tlim=range(0,20))
soln2 = integrateODE(dx~y, dy~x, x=1, y=0, tdur=10)
# plotFun(soln2$y(t)~t, tlim=range(0,10))
# SIR epidemic
epi = integrateODE(dS~ a*S*I, dI ~ a*S*I  b*I, a=0.0026, b=.5, S=762, I=1, tdur=20)

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