lab3_5

def f(x):
    return 1 / (x ** 2 + 4)

def Rectangle(func, X0, Xk, step):
    x = np.arange(X0, Xk + step, step)
    n = np.shape(x)[0]
    h = np.zeros(n)
    for i in range(1, n):
        h[i] = (x[i] - x[i - 1])

    sum = 0
    for i in range(1, np.shape(h)[0]):
        sum += h[i]*func((x[i-1]+x[i])/2)

    return sum

def Trapeze(func, X0, Xk, step):
    x = np.arange(X0, Xk + step, step)
    n = np.shape(x)[0]
    h = np.zeros(n)
    for i in range(1, n):
        h[i] = (x[i] - x[i - 1])

    sum = 0
    for i in range(1, np.shape(h)[0]):
        sum += (func(x[i])+func(x[i-1]))*h[i]

    return sum/2

def Simpson(func, X0, Xk, step):
    x = np.arange(X0, Xk + step, step)
    n = np.shape(x)[0]
    h = np.zeros(n)
    for i in range(1, n):
        h[i] = (x[i] - x[i - 1])

    sum = 0
    for i in range(1, np.shape(h)[0]):
        sum += (func(x[i-1])+4*func((x[i-1]+x[i])/2)+func(x[i]))*(h[i]/2)

    return sum/3

def RungeRombertRichardson(F1, F2, h1, h2, p):
    if h1 < h2:
        return F1 + (F1 - F2) / ((h2 / h1) ** p - 1)
    return F2 + (F2 - F1) / ((h1 / h2) ** p - 1)

X0 = -2; Xk = 2
h1 = 1; h2 = 0.5
rect1 = Rectangle(f, X0, Xk, h1)
rect2 = Rectangle(f, X0, Xk, h2)
rect_RRR = RungeRombertRichardson(rect1, rect2, h1, h2, 1)
trapeze1 = Trapeze(f, X0, Xk, h1)
trapeze2 = Trapeze(f, X0, Xk, h2)
trapeze_RRR = RungeRombertRichardson(trapeze1, trapeze2, h1, h2, 2)
simpson1 = Simpson(f, X0, Xk, h1)
simpson2 = Simpson(f, X0, Xk, h2)
simpson_RRR = RungeRombertRichardson(simpson1, simpson2, h1, h2, 4)

print("Метод прямоугольников:")
print(f"h1 = {h1}: F = {rect1}")
print(f"h2 = {h2}: F = {rect2}")
print(f"Уточнение методом Рунге-Ромберга-Ричардсона: F = {rect_RRR}")
print(f"Погрешности: {abs(rect_RRR-rect1)} и {abs(rect_RRR-rect2)}\n")
print("Метод трапеций:")
print(f"h1 = {h1}: F = {trapeze1}")
print(f"h2 = {h2}: F = {trapeze2}")
print(f"Уточнение методом Рунге-Ромберга-Ричардсона: F = {trapeze_RRR}")
print(f"Погрешности: {abs(trapeze_RRR - trapeze1)} и {abs(trapeze_RRR - trapeze2)}\n")

print("Метод Симпсона:")
print(f"h1 = {h1}: F = {simpson1}")
print(f"h2 = {h2}: F = {simpson2}")
print(f"Уточнение методом Рунге-Ромберга-Ричардсона: F = {simpson_RRR}")
print(f"Погрешности: {abs(simpson_RRR - simpson1)} и {abs(simpson_RRR - simpson2)}")