Numerical Solution of Heat Equation with Singular Robin Boundary Condition

German Lozada-Cruz, Cosme Eustaquio Rubio-Mercedes, Junior Rodrigues-Ribeiro

Abstract


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

Keywords


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

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References


J. M. Arrieta, A. N. Carvalho, and A. Rodriguez-Bernal, A., Attractors for Parabolic Problems with Nonlinear Boundary Condition. Uniform boundeds, Comunications in Partial Differential Equations 25, 1-2, pp. 1-37, 2000.

N. H. Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems. 2nd. ed., Pearson Education, Inc., Upper Saddle River, NJ, 2005.

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. Dewitt, Fundamentals of Heat and Mass Transfer. 7th. ed., John Wiley and Sons, Inc., Danvers, MA, 2007.

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.




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

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Trends in Computational and Applied Mathematics

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