Simulación numérica de la ecuación Lighthill-Whitham-Richards por medio del método de diferencias finitas

Abstract

The Mathematics Program at Escuela Superior Politécnica de Chimborazo (ESPOCH) presents a significant gap in its curriculum plan regarding the study and implementation of numerical methods to solve partial differential equations. Consequently, students within the Mathematics Program lack resources that explain how applied mathematics can be used to address real-world problems across various domains of knowledge. Moreover, there are insufficient documents addressing mathematical models related to vehicular traffic flow. In response to this context, the present research work attempts to analyze the Lighthill-Whitham-Richards mathematical model and the DuFort-Frankel and FTBS finite difference schemes for simulating vehicular traffic flow through its implementation in Python. This study is intended to serve as a guide for the students of the Mathematics Degree at ESPOCH, facilitating their understanding of the discretization process of partial differential equations by means of the finite difference method. To achieve this objective, a qualitative approach with a descriptive scope and a documentary research design was employed. This approach allowed to establish relevant conditions for the stability of both finite difference schemes. The results obtained include a comparison of the LWR equation solution using both the FTBS and DuFort-Frankel schemes.