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
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
1. Authors guarantee the journal the right to be the first publication of the work as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors can set separate additional agreements for non-exclusive distribution of the version of the work published in the journal (eg, place it in an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. The authors have declared to hold all permissions to use the resources they provided in the paper (images, tables, among others) and assume full responsibility for damages to third parties.
4. The opinions expressed in the paper are the exclusive responsibility of the authors and do not necessarily represent the opinion of the editors or the Universidad Nacional.
Uniciencia Journal and all its productions are under Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Unported.
There is neither fee for access nor Article Processing Charge (APC)