Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta

Authors

  • Andresa Pescador UFSC
  • Zilmara Raupp Quadros Oliveira IFC

DOI:

https://doi.org/10.32358/rpd.2016.v2.95

Keywords:

differential equations, applications, numerical methods, analytical solution, numerical solution.

Abstract

This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.

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Author Biographies

Andresa Pescador, UFSC

Bacharel em Matemática e Computação CientíficaMestre em engenharia de materiaisDoutoranda em engenharia de produção (logística)

Zilmara Raupp Quadros Oliveira, IFC

Graduada em licenciatura em matemática pelo IFC campus Sombrio

References

BOYCE, William E; Richard C. DiPrima.Equações Diferenciais Elementares e Problemas de Valores de Contorno. Rio de Janeiro. LTC. 2014.

ÇENGEL, Yunus A., William J. Palm III. Equações Diferenciais. Porto Alegre. AMGH Editora Ltda. 2014.

DIACU, Florin. Introdução a Equações Diferenciais: teoria e aplicações. 2 ª ed. Rio de Janeiro.LCT.1959.

NAGLE, R. Kent, Edward B. Saff, Arthur David Snider. Equações Diferenciais. São Paulo. 8ª edição. Pearson Education do Brasil, 2012.

SIMMONS, George F.; Steven G. Krantz. Equações Diferenciais: Teoria, Técnica e Prática. São Paulo. McGraw-Hill. 2008.

ZILL, Dennis G.. Equações Diferenciais com aplicação em modelagem – tradução da 9ª edição norte-americana. 2 ed. São Paulo. Cengage Learning, 2012.

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Published

2016-04-30

How to Cite

Pescador, A., & Oliveira, Z. R. Q. (2016). Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta. Revista Produção E Desenvolvimento, 2(1), 10–25. https://doi.org/10.32358/rpd.2016.v2.95

Issue

Vol. 2 No. 1 (2016): JANUARY-APRIL

Section

Territorial Affairs

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