Comparative Analysis of Numerical Integration Solutions Pias Method and Newton Cotes Method Using Python Programming Language

Abstract

Irregular areas cannot be solved by ordinary calculus formulas, so it is necessary to use numerical methods such as the Quadrature and Newton-Cotes methods. This research compares numerical integration solutions using the Quadrature method (Rectangular and Trapezoidal) and the Newton-Cotes method (Trapezoidal, Simpson 1/3, Simpson 3/8, and Weddle) with the Python programming language. Manual calculation of the first case study on integrals where the smallest error from the numerical method to the analytical method is achieved by the rectangular method of 0,017. In the second case study of tabular data for manual calculations the author only uses the Simpson 3/8 method with an absolute error for an analytical area of 1.418,583 km2. Whereas in the Python application for the first case study the smallest error was achieved by the Simpson 1/3 and Simpson 3/8 methods with an error of 0, in the sense that these two methods are very accurate to the actual analysis results. In the second case study the smallest error was achieved by the Simpson 1/3 method of 1.039,365 km2. The difference between manual calculations and application results is due to decimal rounding, and the linspace(a,b,n+1) function in the numpy library.