Open AccessNumerical study of different methods applied to the one-dimensional transient heat equation
Author(s) -
Neyva Maria Lopes Romeiro,
Eduardo Oliveira Belinelli,
Jesika Magagnin,
Paulo Laerte Natti,
Eliandro Rodrigues Cirilo
Publication year - 2021
Publication title -
remat
Language(s) - English
Resource type - Journals
ISSN - 2447-2689
DOI - 10.35819/remat2021v7i1id4767
Subject(s) - discretization , heat equation , backward euler method , convergence (economics) , mathematics , transient (computer programming) , finite difference method , consistency (knowledge bases) , stability (learning theory) , crank–nicolson method , numerical analysis , euler method , finite difference , boundary value problem , euler's formula , mathematical analysis , computer science , geometry , machine learning , economics , economic growth , operating system
This article aims to compare the results obtained by applying three numerical methods: Explicit Euler, Crank-Nicolson,and Multi-stage (R11), in the one-dimensional heat diffusion transient equation with different initial and boundary conditions. The discretization process was performed using the finite difference method. In order to guarantee the convergence of the methods used, consistency and stability were verified by Lax theorem. The results are presented in graphs and tables that contain the data of the analytical solution and the numerical solutions. It was observed that the results obtained by R11 method generated solutions with minor errors.