Implementación del método de Crank—Nicolson para resolver la ecuación unidimensional del calor con incertidumbre para estudiantes de cuarto semestre, carrera de Telecomunicaciones de la Escuela Superior Politécnica de Chimborazo.

Abstract

The objective was to implement the Crank-Nicolson method to resolve the one-dimensional heat equation with uncertainty and show this development to fourth-semester students of the Telecommunications Career of the Polytechnic School of Chimborazo. Methodologically, an analysis of the finite difference methods of the finite elements was carried out, and Euler's method was highlighted as a simplification and as a particular case of the finite difference method. Additionally, the Crank-Nicolson method was analyzed and presented as a viable option to solve the problem, solving several application exercises. The analysis of the finite difference method was deepened so that this study serves as a foundation for the subsequent comparison of the efficiencies of both methods. The analysis of errors concomitant to the application of the numerical methods was carried out, and the stability of the methods was analyzed. In addition, the time required for the calculation and the computational cost of implementing the numerical methods were used as comparison parameters. The dissemination of results and the socialization of the application of the method with fourth-semester students of the Telecommunications Career of the Higher Polytechnic School of Chimborazo were carried out. The results of the satisfaction survey posed to the group mentioned above students were presented, and the statistical validity of the results was demonstrated using the calculation of Cronbach's Alpha and a statistical analysis applying the free software R.