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

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

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 fi...

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Main Authors: Neyva Romeiro, Eduardo Oliveira Belinelli, Jesika Magagnin, Paulo Laerte Natti, Eliandro Rodrigues Cirilo
Format: Article
Language:Portuguese
Published: Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) 2021-04-01
Series:REMAT
Subjects:
Mathematical Modeling
Finite Difference Method
Convergence
Online Access:https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4767
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spelling doaj-5d39798327244978880c87ca479694872021-04-21T16:35:38ZporInstituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)REMAT2447-26892021-04-017110.35819/remat2021v7i1id4767Numerical study of different methods applied to the one-dimensional transient heat equationNeyva Romeiro0Eduardo Oliveira Belinelli1Jesika Magagnin2Paulo Laerte Natti3Eliandro Rodrigues Cirilo4State University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, BrazilFederal University of Paraná (UFPR), PPGMNE, Curitiba, PR, BrazilFederal University of Paraná (UFPR), PPGMNE, Curitiba, PR, BrazilState University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, BrazilState University of Londrina (UEL), Department of Math and PGMAC, Londrina, PR, Brazil 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. https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4767Mathematical ModelingFinite Difference MethodConvergence
collection DOAJ
language Portuguese
format Article
sources DOAJ
author Neyva Romeiro
Eduardo Oliveira Belinelli
Jesika Magagnin
Paulo Laerte Natti
Eliandro Rodrigues Cirilo
spellingShingle Neyva Romeiro
Eduardo Oliveira Belinelli
Jesika Magagnin
Paulo Laerte Natti
Eliandro Rodrigues Cirilo
Numerical study of different methods applied to the one-dimensional transient heat equation
REMAT
Mathematical Modeling
Finite Difference Method
Convergence
author_facet Neyva Romeiro
Eduardo Oliveira Belinelli
Jesika Magagnin
Paulo Laerte Natti
Eliandro Rodrigues Cirilo
author_sort Neyva Romeiro
title Numerical study of different methods applied to the one-dimensional transient heat equation
title_short Numerical study of different methods applied to the one-dimensional transient heat equation
title_full Numerical study of different methods applied to the one-dimensional transient heat equation
title_fullStr Numerical study of different methods applied to the one-dimensional transient heat equation
title_full_unstemmed Numerical study of different methods applied to the one-dimensional transient heat equation
title_sort numerical study of different methods applied to the one-dimensional transient heat equation
publisher Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
series REMAT
issn 2447-2689
publishDate 2021-04-01
description 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.
topic Mathematical Modeling
Finite Difference Method
Convergence
url https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4767
work_keys_str_mv AT neyvaromeiro numericalstudyofdifferentmethodsappliedtotheonedimensionaltransientheatequation
AT eduardooliveirabelinelli numericalstudyofdifferentmethodsappliedtotheonedimensionaltransientheatequation
AT jesikamagagnin numericalstudyofdifferentmethodsappliedtotheonedimensionaltransientheatequation
AT paulolaertenatti numericalstudyofdifferentmethodsappliedtotheonedimensionaltransientheatequation
AT eliandrorodriguescirilo numericalstudyofdifferentmethodsappliedtotheonedimensionaltransientheatequation
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