Truncation Error/Examples/Trapezoid Rule

Example of Truncation Error

Let the trapezoid rule be used to integrate $\cos x$ over the closed interval $\closedint 0 {0.8}$ using $8$ subintervals of length $0.1$.

Because $\size {\map{f} x} \le 1$, the truncation error cannot exceed a value given by:

$E \le \size {\dfrac {\paren {0.1}^2 \times 0.8} {12} } = 0.00067$

Proof

Follows from Truncation Error from Trapezoid Rule.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): error: 1. (in numerical computation) Truncation errors
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error: 1. (in numerical computation) Truncation errors