Module: NumericalIntegration

Defined in:
lib/Numerical_Integration.rb

Instance Method Summary collapse

Instance Method Details

#my_exp(x) ⇒ Object 



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# File 'lib/Numerical_Integration.rb', line 53

def my_exp(x)
   return Math.exp(x)
end

#rectangle_method(function, a, b, n) ⇒ Object

Метод левых прямоугольников



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# File 'lib/Numerical_Integration.rb', line 4

def rectangle_method(function, a, b, n)
  h = (b - a).to_f / n #Шаг
  sum = 0.0
  (0..n).each do |i|
    x = a + i*h
    rectangle = function.call(x)
    sum += rectangle
  end
  sum *= h
  return sum
end

#simpsons_method(function, a, b, n) ⇒ Object

Формула Симпсона



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# File 'lib/Numerical_Integration.rb', line 29

def simpsons_method(function, a, b, n)
  h = (b - a).to_f / n
  x = Array.new
  fx = Array.new

  (0..n).each do |i|
    x.push(a + i*h)
    fx.push(function.call(x[i]))
  end

  result = 0.0
  (0..n).each do |i|
    if i == 0 or i == n
      result += fx[i]
    elsif i % 2 != 0
      result += 4* fx[i]
    else
      result += 2 * fx[i]
    end
  end
  result = result * (h / 3)
  return result
end

#trapezoidal_method(function, a, b, n) ⇒ Object

Метод трапеций



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# File 'lib/Numerical_Integration.rb', line 17

def trapezoidal_method(function, a, b, n)
  h = (b - a).to_f / n
  sum = 0.0
  sum += (function.call(a) + function.call(b)) / 2.0
  (1..(n-1)).each do |i|
    sum += function.call(a + i*h)
  end
  sum *= h
  return sum
end