Mathematical Foundations and Principles Behind These Methods

Abstract

This work addresses the definition and historical introduction to numerical methods and the need for their application in engineering. Likewise, the basic concepts of accuracy, precision, convergence, and stability are established, as are the definitions of the different types of errors and how to quantify them. Finally, the Taylor polynomial is a resource for approximating mathematical functions. A subfield of mathematics known as “numerical analysis” uses iterative algorithms to produce numerical solutions to issues where analytical or symbolic mathematics is unable to solve or is inefficient. These algorithms are specifically referred to as numerical methods.