The function ode
provides solvers for systems of ordinary differential equations of the
type:
where
is the vector of state variables. Two solvers are available: the simpler
and faster Euler scheme1 or the more accurate 4-th order Runge-Kutta
method2.
Although many packages already exist to solve ordinary differential
equations in R3, they usually represent the function
either with an R function
or with characters
.
While the representation via R functions
is usually more
efficient, the symbolic representation is easier to adopt for beginners
and more flexible for advanced users to handle systems that might have
been generated via symbolic programming. The function ode
supports both the representations and uses hashed
environments
to improve symbolic evaluations.
The vector-valued function
representing the system can be specified as a vector of
characters
, or a function
returning a numeric
vector, giving the values of the derivatives at time
.
The initial conditions are set with the argument var
and
the time variable can be specified with timevar
.
f <- "x"
var <- c(x=1)
times <- seq(0, 2*pi, by=0.001)
x <- ode(f = f, var = var, times = times)
plot(times, x, type = "l")
f <- "cos(t)"
var <- c(x=0)
times <- seq(0, 2*pi, by=0.001)
x <- ode(f = f, var = var, times = times, timevar = "t")
plot(times, x, type = "l")
f <- c("x", "x*(1+cos(10*t))")
var <- c(x=1, y=1)
times <- seq(0, 2*pi, by=0.001)
x <- ode(f = f, var = var, times = times, timevar = "t")
matplot(times, x, type = "l", lty = 1, col = 1:2)
Guidotti E (2022). “calculus: High-Dimensional Numerical and Symbolic Calculus in R.” Journal of Statistical Software, 104(5), 1-37. doi:10.18637/jss.v104.i05
A BibTeX entry for LaTeX users is