Question

What is the order of the central difference for the mixed derivative (frac{partial^2 u}{partial xpartial y}) while approximated using the Taylor series expansion?

(a) 1

(b) 2

(c) 3

(d) 4

Answer 1

Right answer is (b) 2

To explain: The first term in the truncation error of the central difference for the mixed derivative (frac{partial^2 u}{partial xpartial y} ,is, -(frac{partial^4 u}{partial x^3 partial y})frac{(Delta x)^2}{12}). So, the order of accuracy is 2.