Simple program to approximate y if have dy/dt

eulers_method.rb

def eulers_method(range, h, t, y, &block)
  calculations = []
  calculations << [t, y]
  while t <= range.last
    slope = yield(t, y)    
    yn = y + (slope * h)
    y = yn
    t += h
    calculations << [t, yn]
  end
  
  calculations
end

def gather_values(approximations, points)
  values = []
  points.each do |point|
    approximations.each_with_index do |approx, i|
      if approx[0] >= point
        values << approximations[i]
        break
      end
    end
  end
  values
end

def print_table(data, sample_points, step_sizes)
  data = data.transpose
  cols = step_sizes.unshift("t").map(&:to_s)

  horiz_border = "-"*((cols.length + 1) + (cols.length*9))
  puts horiz_border
  cols.each do |col|
    print "| "
    print col.to_s.ljust(8, " ")
  end
  puts "|"  
  puts horiz_border
  
  sample_points.each_with_index do |t, i|
    print "| "
    print t.to_s.ljust(8, " ")
    data[i].each do |val|
      print "| "
      print val.to_s[0, 6].ljust(8, " ")
    end
    puts "|"
  end
  puts horiz_border
end


if __FILE__ == $PROGRAM_NAME
  sample_points = [1.0, 1.5, 2, 2.5, 3.0]
  step_sizes = [0.1, 0.05, 0.025, 0.01, 0.001, 0.00001]

  data = step_sizes.inject([]) do |accum, step|
    result = eulers_method(1..3, step, 1, 2) { |t, y|
      ((y**2)+(2*t*y))/(3+t**2)
    }
    accum << gather_values(result, sample_points).map { |pair| pair[1] }
  end

  print_table(data, sample_points, step_sizes)
end







#  -----------------------------------------------------------------------
#  | t       | 0.1     | 0.05    | 0.025   | 0.01    | 0.001   | 1.0e-05 |
#  -----------------------------------------------------------------------
#  | 1.0     | 2       | 2       | 2       | 2       | 2       | 2       |
#  | 1.5     | 3.3489  | 3.4188  | 3.5641  | 3.4827  | 3.5025  | 3.4999  |
#  | 2       | 6.1636  | 6.5287  | 7.0069  | 6.8947  | 7.0001  | 6.9998  |
#  | 2.5     | 13.019  | 16.676  | 17.463  | 18.048  | 18.452  | 18.499  |
#  | 3.0     | 38.670  | 84.760  | 140.78  | 287.01  | 1948.1  | 107106  |
#  -----------------------------------------------------------------------