Finite element method for a one-dimensional problems

Abstract

In this thesis, the one-dimensional finite element method was studied for second-order partial differential equation problems to find the approximate solution. This is achieved by dividing the domain of study into small elements, where in each element a simplified formu-lation is sought within each element to establish a system of equations that can be represented as a matrix. The systems of equations for all elements are then assembled to form a large ma-trix, and solving this global system yields the approximate solution. The approximate results and graphical representations were obtained using the Python pro-gramming language.