integrateODE {mosaicCalc}

Integrate ordinary differential equations

Description

A formula interface to integration of an ODE with respect to "t"

Usage

integrateODE(...)

Arguments

...

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=⁠).

Details

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.

Value

a list with splined function of time for each dynamical variable

Examples

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)