Question

Consider the equation \((\frac{\partial u}{\partial y})_{i,j}=(\frac{u_{i,j}-u_{i,j-1}}{\Delta y})\) formulated using the Taylor series expansion. Find the type of equation.

(a) first-order forward difference

(b) first-order rearward difference

(c) second-order forward difference

(d) second-order rearward difference

The question was asked in examination.

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

Answer 1

Correct choice is (b) first-order rearward difference

The explanation is: The equation uses the terms ui,j and its rearward term ui,j-1. So, it represents a rearward difference. The order of accuracy of the equation depends on its truncation error. The truncation error has the least order term \(\frac{-\Delta y}{2}\). So, it is first order accurate.