Generation, evaluation and documentation of numerical integration expressions with polynominal-based approaches

Numerical integration is an important component of mathematical calculations in many problems encountered in various scientific disciplines. Several techniques, including polynomial approximation, can be used to derive integration equations with varying degrees of accuracy. This study aims to produce, evaluate and document numerical integration expressions using methods based on polynomials. The software application developed within the scope of the study uses an input file consisting of information such as polynomial degree and set of points. An LL(1) parser made in compliance with the file syntax using the JavaCC tool transforms this information into a data structure known as an abstract syntax tree. Numerical integration expressions are produced with the help of mathematical calculations performed on the tree structure using a Visitor design pattern. The calculation process consists of stages such as expansion of polynomial expressions, transformation to linear equation system, application of Gaussian elimination method, editing and evaluation of expressions, and transfer of processing steps to PDF document. The integration of application components to Java environments supports the programming processes of integration calculations. In addition, it is evaluated that the documentation of expression generation steps will make a significant contribution to the learning of integration methods.