Question

The truncation error in a finite difference expansion is \(-(\frac{\partial^2 u}{\partial x^2})_{i,j}  \frac{\Delta x}{2}-(\frac{\partial^3 u}{\partial x^3})_{i,j} \frac{(\Delta x)^3}{6}\). What is the order of accuracy of the finite difference equation?

(a) 1

(b) 2

(c) -2

(d) -1

The question was posed to me during a job interview.

My question is taken from Finite Difference Method in division Finite Difference Methods of Computational Fluid Dynamics

Answer 1

The correct option is (a) 1

Explanation: The lowest order term in the truncation error given is \(\frac{\Delta x}{2}\), which is of the order 1. This defines the order of accuracy of the equation. So, the order of accuracy here is 1.