Modelación de ecuaciones diferenciales parciales mediante diferencias finitas y elementos finitos como herramientas de apoyo para estudiantes de cuarto semestre carrera de Física de la Escuela Superior Politécnica de Chimborazo.

Abstract

The aim was to model partial differential equations using finite differences and finite elements as a support tool for students in the fourth semester of the Physics career at Polytechnic School of Chimborazo. Physics students continuously require the modeling of elliptic and parabolic differential equations, which have a difficult solution by exclusively analytical methods when the boundary and initial conditions are not simple. Therefore, the need to apply numerical methods, including the numerical and the finite elements methods and analysis which provides a better understanding of the matter. Bibliographic information on the analytical resolution of the methods was collected to be applied in MATLAB. In addition, modeling information was collected using the differential equation software. On the other hand, a survey was developed to determine the perception of students about teaching partial differential equations, 6 main codes were obtained for each of the partial differential equations (parabolic, elliptic and hyperbolic) for the finite element and finite differential methods, which are recommended to be applied in the teaching of Physics.