Runge-Kutta with y = exp(x^2), y' = 2 x y, x: 0 to 1

#!/usr/bin/ruby
# coding: utf-8
def df(x, y) 2 * x * y end
n = 128
ret = []
ret << [0.0, 1.0]
h = 1.0 / n
n.times do |i|
  k1 = h * df(ret[i][0], ret[i][1])
  k2 = h * df(ret[i][0] + h / 2, ret[i][1] + k1 / 2)
  k3 = h * df(ret[i][0] + h / 2, ret[i][1] + k2 / 2)
  k4 = h * df(ret[i][0] + h, ret[i][1] + k3)
  ret << [(i + 1) * h, ret[i][1] + (k1 + 2 * k2 + 2 * k3 + k4) / 6]
end
open('outpu.dat', 'w') do |f|
  ret.each {|x, y| f.puts "#{x} #{y}"}
end