# Reducing Errors in Numerical Analysis

Truncation error can be reduced by using a better numerical model that usually increases the number of arithmetic operations. Learn more about how to reduce errors in numerical analysis.

Truncation error is a difference between the true (analytical) derivative of a function and its derivative obtained by numerical approximation. It is important to understand its nature and order when using numerical methods or algorithms and calculating with finite precision, as approximation or rounding and truncation errors are introduced. A newly developed method is worthless without error analysis, and it doesn't make sense to use methods that introduce errors with magnitudes greater than the effects to be measured or simulated. On the other hand, using a method with very high precision may be computationally too expensive to justify the gain in accuracy.

The step size is normally estimated according to the truncation error in the kth (current) iteration, and the remaining term is generally expressed as Rn%3do (hn+), which shows that the truncation error is proportional to the size of the step, h, raised to n+1, where n is the number of terms included in the expansion. A high truncation error is an indicator that the original process LCA model is incomplete, encouraging the use of hybrid LCA to replace the process LCA when comparing different alternatives. The allowed truncation error, known as tolerance, is typically used to control the accuracy of the integration. To reduce truncation error, it is necessary to use a better numerical model that usually increases the number of arithmetic operations.

After estimating the truncation error of the integration in the (k+) th iteration, a decision can be made as to whether to accept or reject the step size. The global truncation error is the agglomeration of the local truncation error in all iterations, assuming a perfect knowledge of the true solution in the initial time step. In conclusion, it is important to understand how truncation errors are introduced when using numerical methods or algorithms and calculating with finite precision. To reduce these errors, it is necessary to use a better numerical model that usually increases the number of arithmetic operations.

The allowed truncation error, known as tolerance, should be used to control the accuracy of the integration. Additionally, it is important to estimate and consider global truncation error when making decisions about step size.

##### Charlotte Wilson

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