MediumCalculusca-067

Mixed Partial Finite Difference

Problem

Approximate the mixed partial derivative of f(x, y) = x^m * y^n at (x, y) with the four-point central stencil:

f_xy ≈ (f(x+h, y+h) - f(x+h, y-h) - f(x-h, y+h) + f(x-h, y-h)) / (4*h^2)

Use h = 1e-4. The analytic value is m*n*x^(m-1)*y^(n-1).

Hint

The stencil is a symmetric cross difference; divide by 4 h squared.

case 1

in: [2,3,1,2]

expected: 24.00000003177638

case 2

in: [1,1,3,4]

expected: 1.00000003833145

case 3

in: [2,2,0,5]

expected: 0

case 4

in: [3,1,2,1]

expected: 12.00000001588819

Starter codePython

def mixed_partial(m, n, x, y, h=1e-4):
    # f(x, y) = x**m * y**n
    # Your code here
    pass

4 test cases · run your code against them in the editor