runge.kutta numerically solves a differential equation by the
fourth-order Runge-Kutta method.
runge.kutta(f, initial, x)A vector of values of y as solution of the function f
corresponding to the values in x.
A function dy/dx=func(y,x).
The initial value of y.
A vector of values of x for which the values or
y are required.
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)
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