(408) Numerical Integration Methods طرق التكامل العددي - I. Abdel Karim, Abbas (معهد التخطيط القومى, 2024)
The work entitled “Numerical Integration Methods” examines numerical integration as one of the fundamental mathematical techniques used to estimate the values of integrals that are difficult or impossible to solve analytically. The significance of this field arises from its extensive applications in statistics, economics, engineering, physics, and applied sciences, where many practical problems require approximate computational methods for measuring areas, changes, and quantitative relationships. The study aims to provide a theoretical and practical framework for numerical integration methods and to explain the mathematical principles underlying different approximation techniques. It further seeks to clarify the criteria for selecting an appropriate method according to the characteristics of the mathematical function under investigation and the required level of precision. The research also examines the relationship between estimation error and the number of intervals or points used in numerical procedures. The analysis is based on concepts from numerical analysis and mathematical computation, emphasizing commonly used methods of numerical integration such as the Trapezoidal Rule, Simpson’s Rule, Newton–Cotes formulas, and other approximation techniques widely applied in scientific research. The study additionally discusses the mathematical foundations of approximation errors and methods used to evaluate the accuracy of numerical estimates. The findings indicate that selecting a suitable numerical integration technique depends on the characteristics of the target function and the regularity of the available data. Increasing the number of intervals generally improves estimation accuracy; however, it may also increase computational requirements and mathematical complexity. The analysis further suggests that inappropriate methods may produce cumulative errors affecting the reliability of final results.