Numerical Solution of Heat Equation with Singular Robin Boundary Condition

Autores

DOI:

https://doi.org/10.5540/tema.2018.019.02.209

Palavras-chave:

Eigenvalue Problems, Finite Difference Method, Robin Boundary Conditions, Numerical Solutions

Resumo

In this work we study the numerical solution of one-dimensional heat
diffusion equation with a small positive parameter subject to Robin boundary conditions. The simulations examples lead us to conclude that the numerical solutions
of the differential equation with Robin boundary condition are very close of the
analytic solution of the problem with homogeneous Dirichlet boundary conditions
when tends to zero

Biografia do Autor

German Lozada-Cruz, S~ao Paulo State University - UNESP.

Institute of Biosciences,
Humanities and Exact Sciences, Departament of Mathematics.

Cosme Eustaquio Rubio-Mercedes, Mato Grosso do Sul State University - UEMS

Engineering Physics Programs

Junior Rodrigues-Ribeiro, São Paulo State University - USP

Institute of Mathematics Sciences and Computing

Referências

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W. E. Boyce and R. C. DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems. 7th. ed., John Wiley and Sons, Inc., New York, 2001.

G. Buttazzo, M. Giaquinta, S. Hildebrandt, One-dimensional variational problems. An introduction. Oxford Lecture Series in Mathematics and its Applications, 15. The Clarendon Press, Oxford University Press, New York, 1998.

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

J. A. Cuminato and Jr. M. Meneguette, Discretiza¸c~ao de Equa¸c~oess Diferenciais Parciais: T´ecnicas de Diferen¸cas Finitas. 1. ed. Rio de Janeiro: SBM, 2013.

D. Henry, Geometry theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlim, 1981.

H. E. Hernández-Figueroa and C. E. Rubio-Mercedes,Transparent Boundary for the Finite-Element Simulation of Temporal Soliton Propagation, IEEE Transaction on Magnetics, Vol. 34, No. 5, 1998.

J. D. Hoffman Numerical Methods for Engineers and Scientists. 2nd. ed., Marcel Dekker, Inc., New York, 2001.

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Publicado

2018-09-12

Como Citar

Lozada-Cruz, G., Rubio-Mercedes, C. E., & Rodrigues-Ribeiro, J. (2018). Numerical Solution of Heat Equation with Singular Robin Boundary Condition. Trends in Computational and Applied Mathematics, 19(2), 209. https://doi.org/10.5540/tema.2018.019.02.209

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Artigo Original