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 first-order form. Each dynamical equation uses
a formula interface with the variable name given on the left-hand 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 spline-generated 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*(1-x/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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