Error rules in numerical methods refer to the guidelines or formulas used to estimate or calculate the error involved in the approximation or solution obtained through the method. These rules are important in assessing the accuracy and reliability of numerical methods and can help determine the level of confidence in the results obtained.

Some common error rules used in numerical methods include:

1. Absolute Error: This rule calculates the absolute difference between the exact or known value and the approximate value obtained through the numerical method.

2. Relative Error: Relative error is the ratio of the absolute error to the exact or known value. It represents the error as a percentage of the exact value and is used to compare errors across different problems.

3. Order of Convergence: This rule is used to determine the rate at which the error decreases as the step size or iteration increases. It helps assess the efficiency and accuracy of the numerical method.

4. Taylor Series Expansion: Taylor series expansion is used to approximate a function using a polynomial. The error involved in this approximation can be estimated using the remainder term in the Taylor series.

5. Richardson Extrapolation: This rule is used to improve the accuracy of an approximation by combining multiple approximations with different step sizes. It helps estimate the error and provides a more accurate solution.

6. Error Propagation: Error propagation refers to how errors in the input data or parameters of a numerical method affect the accuracy of the final result. It helps assess the sensitivity of the method to errors in the input.

By applying these error rules, numerical analysts can evaluate the accuracy and reliability of numerical methods and make informed decisions about the suitability of these methods for specific applications.