2. Write a computer code to implement the Composite Trapezoidal Rule quadrature

Question

2. Write a computer code to implement the Composite Trapezoidal Rule quadrature to approximate the definite integral b, where using the equally spaced points zo = a, = xo + h, x,-zo + 2h, . .. ,.EN 11 = (b-a)/N (a) Test your code with f(x) = 1/(1+1)2 in [0,2] by computing the error l[f-Th[nl for h = 2/20, 2/40.2/80, and verify that T, has a convergent trend at the expected. quadratic rate. (b) Let f(x)-2/3 in [O, 1]. Compute T1/N for N = 16, 32, 64, 128, Do you see a second order convergence to the exact value of the integral? Explain

Explanation / Answer

def Trap(a, b, n, h):

area = (f(a) + f(b))/2.0

for i in xrange(1, n):

x = a + i*h;

area = area + f(x)

area = area*h

return area

# End of Trap

# Purpose: Compute value of function to be integrated

def f(x):

return_val = x*x + 1

return return_val

# End of f

# main function

print "Enter a, b, and n"

line = stdin.readline()

strings = line.split()

a = float(strings[0])

b = float(strings[1])

n = int(strings[2])

h = (b-a)/n

area = Trap(a, b, n, h)

print "With n =", n, "trapezoids, our estimate"

print "of the area from", a, "to", b, "= %.15f" % area

# End of main

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