Numerical study of different methods applied to the one-dimensional transient heat equation

Neyva Maria Lopes Romeiro Romeiro; Eduardo Oliveira Belinelli; Jesika Magagnin; Paulo Laerte Natti; Eliandro Rodrigues Cirilo

doi:10.35819/remat2021v7i1id4767

Authors

Neyva Maria Lopes Romeiro Romeiro State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil https://orcid.org/0000-0002-3249-3490
Eduardo Oliveira Belinelli Federal University of Paraná (UFPR), PPGMNE, Curitiba, PR, Brazil https://orcid.org/0000-0002-5925-086X
Jesika Magagnin Federal University of Paraná (UFPR), PPGMNE, Curitiba, PR, Brazil https://orcid.org/0000-0003-2719-3124
Paulo Laerte Natti State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil https://orcid.org/0000-0002-5988-2621
Eliandro Rodrigues Cirilo State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil https://orcid.org/0000-0001-7530-1770

DOI:

https://doi.org/10.35819/remat2021v7i1id4767

Keywords:

Mathematical Modeling, Finite Difference Method, Convergence

Abstract

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.

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Author Biographies

Neyva Maria Lopes Romeiro Romeiro, State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil

http://lattes.cnpq.br/4461273355568982
Eduardo Oliveira Belinelli, Federal University of Paraná (UFPR), PPGMNE, Curitiba, PR, Brazil

http://lattes.cnpq.br/7765410891571937
Jesika Magagnin, Federal University of Paraná (UFPR), PPGMNE, Curitiba, PR, Brazil

http://lattes.cnpq.br/3679804525555664
Paulo Laerte Natti, State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil

http://lattes.cnpq.br/9638679509810719
Eliandro Rodrigues Cirilo, State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil

http://lattes.cnpq.br/4013438197275949

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