Performance of Closed Newton-Cotes methods and alternative extended Simpson’s Rule method for solving complex integration functions / Nurul Fatihah Kamaruddin

In mathematics, numerical integration is particularly important. In this project, there are five numerical integration methods involved which come from Closed Newton- Cotes Methods (Trapezoidal Rule, Simpson’s 1/3 Rule, Simpson’s 3/8 Rule, Boole’s Rule) and Alternative Extended Simpson’s Rule. The main goal of this research is to evaluate the effectiveness of Closed Newton-Cotes Methods and Alternative Extended Simpson's Rule. Based on error analysis and CPU time, the best method is chosen. The effective method will be determined based on the lowest percentage error and CPU times. The best method in total is determined based on the performance of percentage error. To choose the best method, the programme MATLAB R2022a is used, and the outcomes are compared. SigmaPlot 14.0 software has been included to display the performance profile of each method. In the end, it is emphasised that Simpson's 1/3 is the best method with subinterval of n = 96 in term of error analysis. While Alternative Extended Simpson’s Rule with subinterval of n = 12 is the most effective method based on CPU Times performance.