Question

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

(a) 1

(b) 2

(c) 3

(d) 4

I got this question in final exam.

The above asked question is from Finite Difference Method in division Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Right answer is (b) 2

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