runge.kutta {rmutil} | R Documentation |
runge.kutta
numerically solves a differential equation by the
fourth-order Runge-Kutta method.
runge.kutta(f, initial, x)
f |
A function dy/dx=func(y,x) . |
initial |
The initial value of y . |
x |
A vector of values of x for which the values or
y are required. |
A vector of values of y
as solution of the function f
corresponding to the values in x
.
J.K. Lindsey
fn <- function(y,x) (x*y-y^2)/x^2 soln <- runge.kutta(fn,2,seq(1,3,by=1/128)) ## exact solution exact <- seq(1,3,by=1/128)/(0.5+log(seq(1,3,by=1/128))) rbind(soln, exact)