# Reducing Truncation Error in Numerical Analysis and Scientific Computation

Learn how to reduce truncation errors in numerical analysis and scientific computation with this comprehensive guide. In numerical analysis and scientific computation, truncation error is the error caused by the approximation of a mathematical process. Similar to a rounding error, a truncation error occurs when a large number is reduced to fit a data type. To reduce the truncation error, we can make repeated iterations. However, we must also take into account the rounding error.

To calculate the local truncation error, we apply an equation. To obtain a global truncation error limit, we can use the second-order Adams-Moulton algorithm. Given an infinite series, we can find the truncation error of x% 3d0,75 if only the first three terms of the series are used. The error caused by choosing a finite number of rectangles instead of an infinite number is a truncation error in the mathematical process of integration.

We can reduce the truncation error of the numerical integration rule by using a recursive algorithm. If the step size is reduced by half, the truncation error of the central difference approximation is reduced by four. For miscible displacements, a Taylor serial analysis of truncation error can provide a good estimate of longitudinal numerical diffusivity in finite difference and finite volume schemes. Truncation, also called derivation, is a technique that broadens the search to include multiple word endings and spelling.

If the step size h between two adjacent values Ik becomes smaller, the truncation error of the numerical integration rule decreases. ##### Charlotte Wilson

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