runge.kutta {rmutil}

Runge-Kutta Method for Solving Differential Equations

Description

runge.kutta numerically solves a differential equation by the fourth-order Runge-Kutta method.

Usage

runge.kutta(f, initial, x)

Arguments

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.

Value

A vector of values of y as solution of the function f corresponding to the values in x.

Author(s)

J.K. Lindsey

Examples

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)