Treffer: Software Development and Best Practices: Introduction to Programming Languages Used in Numerical Methods

The growth of science and technology has made it feasible to create software programmes that can quickly solve problems that used to take a long time to resolve. Non-linear equations frequently arise in various complex difficulties that we encounter in our everyday existence. This study aims to assess the effectiveness of the Secant technique and the Newton Raphson method in solving non-linear equations in Python. The programming test was conducted three times with different coefficients and starting values. Another objective of this research is to assess the effectiveness of numerical integration utilising Simpson's methods through the utilisation of Pascal-based software programmes. Two variants of the numerical integration method are the Simpson method. After reviewing research data, the Simpson 1/3 approach proved to be the most accurate strategy to estimate integral values using exponential, polynomial, and trigonometric functions within the 0.001%−0.005% range. The Simpson 1/3 technique runs Pascal faster than Simpson 3/8.