Last chance! 50% off unlimited learning
Sale ends in
A formula interface to integration of an ODE with respect to "t"
integrateODE(...)a list with splined function of time for each dynamical variable
A dynamics object (see makeODE()) and/or arguments giving additional formulas for dynamics in other variables,
assignments of parameters, assignments of initial conditions, the start and end times of the
integration (through domain()), and the step size (through dt=).
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.
soln = integrateODE(dx~r*x*(1-x/k), k=10, r=.5, domain(t=0:20), x=1)
soln$x(10)
soln$x(30) # outside the time interval for integration
traj_plot(x(t)~t, soln, domain(t=0:10))
soln2 = integrateODE(dx~y, dy~-x, x=1, y=0, domain(t=0:10))
traj_plot(y(t)~t, soln2)
SIR <- makeODE(dS~ -a*S*I, dI ~ a*S*I - b*I, a=0.0026, b=.5, S=762, I=1)
epi = integrateODE(SIR, domain(t=0:20))
traj_plot(I(t) ~ t, epi)
Run the code above in your browser using DataLab