2.4 Analysis of Finite Difference Methods

2.4.2 Truncation Error of Central Difference Approximation

What is the truncation error and order of accuracy of the central difference approximation $$\delta _{2x}U_ i = \frac{U_{i+1}-U_{i-1}}{2\Delta x}$$ of $$U_{x_ i}$$

Exercise 1

Answer: The truncation error can be computed by inserting the Taylor series into the finite difference approximation and cancelling the appropriate terms. Since the error is $$\mathcal{O}(\Delta x^2)$$, the approximation is second-order accurate.