Application of the Neumann Boundary Conditions to One and Two Dimensional Analytical Solution of Wave Equation

This project aims the implementation of an approximate analytical solution for the wave equation in one and two dimensional domains for Neumann Boundary Conditions (NBC), which the gradient of the primary variable is known within the boundary domain and, for the proposed implementation, is defined as a periodic function of time. Fourier series was used to determine the approximated solutions for the wave equations and it was implemented in Python 3.7 programming language. The Object-Oriented Paradigm (OOP) approach was used to provide flexibility for the implementation, resulting in an Application Programming Interface (API) that provides functionalities such as increasing the number of approximation terms and several visualization tools. The results are presented considering two different frequencies and compared to the Finite Difference Method (FDM) solution, leading to root-mean-squared-errors of order \(10^{-6}\) (Pa).