Added Simpson Rule to Maths

Author: ltdouthit

Maths/SimpsonRule.py

@@ -0,0 +1,47 @@
+
+'''
+Numerical integration or quadrature for a smooth function f with known values at x_i
+
+This method is the classical approch of suming 'Equally Spaced Abscissas' 
+
+method 2: 
+"Simpson Rule"
+
+'''
+
+def method_2(boundary, steps):
+# "Simpson Rule"
+# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
+h = (boundary[1] - boundary[0]) / steps
+a = boundary[0]
+b = boundary[1]
+x_i = makePoints(a,b,h)
+y = 0.0
+y += (h/3.0)*f(a)
+cnt = 2
+for i in x_i:
+y += (h/3)*(4-2*(cnt%2))*f(i)
+cnt += 1
+y += (h/3.0)*f(b)
+return y
+
+def makePoints(a,b,h):
+x = a + h
+while x < (b-h):
+yield x
+x = x + h
+
+def f(x): #enter your function here
+y = (x-0)*(x-0)
+return y
+
+def main():
+a = 0.0 #Lower bound of integration
+b = 1.0#Upper bound of integration
+steps = 10.0#define number of steps or resolution
+boundary = [a, b]#define boundary of integration
+y = method_2(boundary, steps)
+print 'y = {0}'.format(y)
+
+if __name__ == '__main__':
+ main()