ode | R Documentation |
Solves a numerical or symbolic system of ordinary differential equations.
ode( f, var, times, timevar = NULL, params = list(), method = "rk4", drop = FALSE )
f |
vector of |
var |
vector giving the initial conditions. See examples. |
times |
discretization sequence, the first value represents the initial time. |
timevar |
the time variable used by |
params |
|
method |
the solver to use. One of |
drop |
if |
Vector of final solutions if drop=TRUE
, otherwise a matrix
with as many
rows as elements in times
and as many columns as elements in var
.
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
Other integrals:
integral()
## ================================================== ## Example: symbolic system ## System: dx = x dt ## Initial: x0 = 1 ## ================================================== f <- "x" var <- c(x=1) times <- seq(0, 2*pi, by=0.001) x <- ode(f, var, times) plot(times, x, type = "l") ## ================================================== ## Example: time dependent system ## System: dx = cos(t) dt ## Initial: x0 = 0 ## ================================================== f <- "cos(t)" var <- c(x=0) times <- seq(0, 2*pi, by=0.001) x <- ode(f, var, times, timevar = "t") plot(times, x, type = "l") ## ================================================== ## Example: multivariate time dependent system ## System: dx = x dt ## dy = x*(1+cos(10*t)) dt ## Initial: x0 = 1 ## y0 = 1 ## ================================================== 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, var, times, timevar = "t") matplot(times, x, type = "l", lty = 1, col = 1:2) ## ================================================== ## Example: numerical system ## System: dx = x dt ## dy = y dt ## Initial: x0 = 1 ## y0 = 2 ## ================================================== f <- function(x, y) c(x, y) var <- c(x=1, y=2) times <- seq(0, 2*pi, by=0.001) x <- ode(f, var, times) matplot(times, x, type = "l", lty = 1, col = 1:2) ## ================================================== ## Example: vectorized interface ## System: dx = x dt ## dy = y dt ## dz = y*(1+cos(10*t)) dt ## Initial: x0 = 1 ## y0 = 2 ## z0 = 2 ## ================================================== f <- function(x, t) c(x[1], x[2], x[2]*(1+cos(10*t))) var <- c(1,2,2) times <- seq(0, 2*pi, by=0.001) x <- ode(f, var, times, timevar = "t") matplot(times, x, type = "l", lty = 1, col = 1:3)
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