Techniques for reducing numerical error in the calculation of numerical integration: a comparative study

Abstract

Numerical integration is one of the most important tools in scientific, engineering, and mathematical applications to reduce the rate of numerical error, which makes the results inaccurate and thus affects the efficiency of these applications. This study aims to review previous literature and extract the most important results for comparison between them and to know the factors that affect numerical integration methods, whether the type of function, the type of application, the size of the function, the number of points of the function, the extent of the function’s spacing, the flexibility and accuracy of calculations, and the ease of use and stability of numerical integration methods. Such as Gaussian integration methods, adaptive integration methods, Simpson methods, and Newton-Curtis Rolle Monte Carlo methods. Through a methodology, more methodologies were adopted, such as the descriptive methodology in describing integration methods and the factors affecting them, and the quantitative methodology in collecting data from previous studies and drawing conclusions related to the factors affecting numerical integration methods in terms of efficiency, accuracy, flexibility and stability, and evaluating these results and the factors affecting them by reviewing more than 100 studies. Related to the topic, using comparative methodology to compare the results of those studies and analytical methodology to analyze and evaluate the results. The results indicated that for the total weight, adaptive integration ranked first with a rate of 87%, followed by the Simpson-Role method with 85%, then Gauthian integration with a rate of 84%, then integration with 82%, and Newton-Curtz-Rolle method with 85%.