Computational aspects of the finite difference method for the time-dependent heat equation
DOI:
https://doi.org/10.15359/ru.33-1.7Keywords:
Heat equation, finite difference method, computational implementation, MATLABAbstract
In this paper we describe in detail an algorithm for the efficient computational implementation of the finite difference method (FDM) in the two-dimensional time-dependent heat equation with non-homogeneous Dirichlet boundary conditions. The MATLAB® software was used to validate the method mentioned here; however, the processes are presented independently from the programming language. Finally, numerical results are presented to validate the proposed algorithm.
References
Carslow, H. S., y Jaeger, J. C. (1959). Conduction of Heat in Solids. Segunda edición. Inglaterra: Oxford University Press.
Ciarlet, P. G. (1995). Introduction to numerical linear algebra and optimisation. Estados Unidos: Cambrige University Press.
Ciarlet, P. G. (2002). The finite Element Method for Elliptic Problems. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9780898719208
Datta, B. N. (2010). Numerical Linear Algebra and Applications. Segunda Edición. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9780898717655
Demmel, J. W. (1997). Applied Numerical Linear Algebra. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9781611971446
Evans, L. C. (2010). Partial Differential Equations. Segunda edición. Estados Unidos: American Mathematical Society.
Guzmán, J., Shu, C-W., y Sequeira, F. A. (2017). H(div) conforming and DG methods for the incompressible Euler's equations. IMA Journal of Numerical Analysis, 37(4), 1733-1771. doi: https://doi.org/10.1093/imanum/drw054
Haberman, R. (1998). Elementary Applied Partial Differential Equations, With Fourier Series and Boundary Value Problems. Tercera edición. Estados Unidos: Prentice-Hall.
Hahn, B. H., y Valentine D. T. (2016). Essential MATLAB for Engineers and Scientists. Sexta edición. Estados Unidos: Elsevier.
LeVeque, R. J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations, Steady-State and Time-Dependent Problems. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9780898717839
Morton, K. W., y Mayers, D. F. (2005). Numerical Solution of Partial Differential Equations. Segunda edición. Inglaterra: Cambrige University Press. doi: https://doi.org/10.1017/CBO9780511812248
Quinn, M. J. (2003). Parallel Programming in C with MPI and OpenMP. Estados Unidos: McGraw-Hill.
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems. Segunda Edición. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9780898718003
Strikwerda, J. C. (2004). Finite Difference Schemes and Partial Differential Equations. Segunda edición. Estados Unidos: SIAM. doi: https://doi.org/10.1137/1.9780898717938
Thomas, J. W. (1995). Numerical Partial Differential Equations: Finite Difference Methods. Estados Unidos: Springer-Verlag. doi: https://doi.org/10.1007/978-1-4899-7278-1
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