This tag is for questions relating to truncation error, which is the difference between the true (analytical) derivative of a function and its derivative obtained by numerical approximation.
In numerical analysis and scientific computing, truncation error is the difference between a truncated value and the actual value. A truncated quantity is represented by a numeral with a fixed number of allowed digits, with any excess digits "chopped off" (hence the expression "truncated").
As an example of truncation error, consider the speed of light in a vacuum. The official value is $~299,792,458~$ meters per second. In scientific (power-of-$~10$) notation, that quantity is expressed as $~2.99792458 \times 10^8~$. Truncating it to two decimal places yields $~2.99 \times 10^8~$. The truncation error is the difference between the actual value and the truncated value, or $~0.00792458 \times 10^8~$. Expressed properly in scientific notation, it is $~7.92458 \times 10^5~$.
Often, truncation error also includes discretization error, which is the error that arises from taking a finite number of steps in a computation to approximate an infinite process. For example, in numerical methods for ordinary differential equations, the continuously varying function that is the solution of the differential equation is approximated by a process that progresses step by step, and the error that this entails is a discretization or truncation error.
Occasionally, round-off error (the consequence of using finite precision floating point numbers on computers) is also called truncation error, especially if the number is rounded by truncation.
References:
https://en.wikipedia.org/wiki/Truncation_error
https://en.wikipedia.org/wiki/Truncation_error_(numerical_integration)
https://en.wikiversity.org/wiki/Numerical_Analysis/Truncation_Errors
