Question

What is a truncation error? How can Taylor's series be used to determine truncation error? Explain with the help of an example.

Answer 1

A truncation error is the difference between the true value (obtained by analytical methods) and numerical value. Taylor's series can help to find the numerical derivative.

Example: series

$$\frac12+\frac14+\frac18+...+\frac1{2^n}$$

has an analytical sum of 1.

However, when we compute it, and take say the first 7 terms, the sum is 0.992. The truncation error is, therefore,

$$\Epsilon=1-0.992=0.008.$$