# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from math import exp, sin, cos, log10

def f(x):

return exp(sin(2*x))

def fprime(x):

return 2*exp(sin(2*x))*cos(2*x)

def calc_fd(f,x,h):

fd = (f(x+h) - f(x))/h

return fd

def calc_cd(f,x,h):

cd = (f(x+h/2) - f(x-h/2))/h

return cd

if __name__ == '__main__':

x = 0.5

an = fprime(x)

hs = [10**(-i) for i in range(1,12)]

fds = [abs(calc_fd(f,x,h) - an) for h in hs]

cds = [abs(calc_cd(f,x,h) - an) for h in hs]

rowf = "{0:1.0e} {1:1.16f} {2:1.16f}"

print("h abs. error in fd abs. error in cd")

for h,fd,cd in zip(hs,fds,cds):

print(rowf.format(h,fd,cd))