Comparison of the Trapezoidal Rule and Simpson’s Rule

Abstract

This paper focuses on the numerical integration that aimed to compare the rate of performance or the rate of accuracy of the Trapezoidal rule and Simpson’s rule. The objective of this project is to estimate which one of the values by using the Trapezoidal Rule. Furthermore, to analyse the value by using Simpson’s Rule. Lastly, to compare the Trapezoidal Rule performance or accuracy rate against Simpson's Rule. The three equations employed in this study will be used in Maple software, and the results will be obtained once the equations have been numerically solved. A comparison between the numerical solutions of the Trapezoid rule and Simpson's rule is also possible because of the numerical solution analysis results. In the event where the division condition is only even, Simpson's rule provides a lower error number than other ways, while other approaches provide less precision. As a result, the Simpson technique is the most trustworthy approach for computing definite integrals and is more accurate than the Trapezoid rule. The error value of the data is based on the difference between exact and approximate values. The result of this paper isshown that Simpson’s rule is to contribute more precise correct value, rather than Trapezoidal’s rule. However, Maple’s software is the better instrument to consume for any mathematical problem solving that needs more than six decimal places, instead of Matlab’s software to use in future work such as on the application of autopilot