Numerical Insights on Vector Fields: Python and MATLAB-Based Numerical Methods for Partial Differential Equations

Vector analysis is a mathematical concept powerful enough to represent various theories, notions, and concepts under engineering and physics. This project focuses on specific operations in vector calculus, namely Divergent and Curl, which are known to be used in the discipline of fluid dynamics, electric and magnetic fields, as well as weather patterns. A Python program was created and used as a tool to obtain the divergence and curl of the given vector fields, which are supported by manual computations and the use of MATLAB as another platform. The acquired results for the three aforementioned methods showed similar values for each of the vector fields. Performing the manual computation showed the mathematical approach in analyzing the concept of divergence and curl, while Python and MATLAB presented how these are acquired through different programming languages. Throughout the project, the research highlighted the significance and numerous scientific applications of vector analysis which may be utilized in future discoveries in the field of engineering.