寻找导数的二阶精确方案

Question

So I'm doing a class project and have to plot a numerical approximation of the derivative of f(x)=x*arctan(x) using the second order accurate scheme, f(xi) ≈(f(xi+1) − f(xi−1))/2h oh and also plot f(x)

I've done this so far:

from numpy import *
from matplotlib.pylab import *
a=0
b=2
n=100
h=(b-a)/n
def f(x):
    f=x*arctan(x)
    return(f)
def dydx(x):
    d=(f(x+h)-f(x-h))/2*h
    return(d)
x=linspace(a,b,n+1)
plot(x,f(x),'b')
plot(x,dydx(x),'r--')

the problem i am receiving is that the graph for my derivative is coming out at a significantly lesser value than it should be (ie limit at 0.0006 instead of 1.6 ) - how do I fix this?

Answer 1

I'm not the brightest light when it comes to math problems, so I might misunderstand your question, but the problem couldn't perhaps be that you simply forgot to place 2*h inside of some parenthesis?

So instead of: d=(f(x+h)-f(xh))/2*h Try: d=(f(x+h)-f(xh))/(2*h)