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Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions

Received: 11 November 2015     Accepted: 22 November 2015     Published: 14 December 2015
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Abstract

In this paper we have introduced Numerical techniques to solve a two dimensional Poisson equation together with Dirichlet boundary conditions. Specifically two methods are used for the purpose of numerical solution, viz. Finite difference method and Finite element method. The implementation of the solutions is done using Microsoft Office Excel worksheet or spreadsheet. The numerical solutions obtained by these two methods are also compared with each other graphically in two and three dimension.

Published in American Journal of Applied Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.ajam.20150306.19
Page(s) 297-304
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Dirichlet Boundary Conditions, Finite Difference Method, Finite Element Method, Poisson Equation, Spreadsheet

References
[1] Alfio Quarteroni, Numerical models for differential problems (2nd edition), Springer-Verlag, Italia, 2014.
[2] Chapra Canal, Numerical methods for engineers (4th edition), The McGraw Hill Companies, 2001.
[3] Erwin Kreyzing, Advanced Engineering Mathematics (9thedition), 2006 John Wiley and Sons, Inc.
[4] G. Evans, J. Blackledge and P. Yardley, Numerical methods for partial differential equations, Springer-Verlag London Limited 2000.
[5] J. David Logan, A first course in DEs, 2006 Springer Science + Business Media. Inc.
[6] Lichard L. Burden and J. Douglas Faires, Numerical analysis (9th edition), 2011, 2005, 2001 Brooks/Cole, Cengage Learning, 20 Channel Center Street Boston, MA02210, USA.
[7] Mark A. Lau and Sastry P. Kuruganty, Spreadsheet implementation for solving boundary value problem in electromagnetic, spreadsheet in education (eJSiE) 4(1), 2001.
[8] Parag V. Patil and Dr. J.S.V.R. Krishna Prasad, Numerical solution for two dimensional Laplace equation with Dirichlet boundary conditions, Volume 6, Issue 4 (May - June 2013), PP 66-75.
[9] Ravi P. Agarwal and Donal O'Regan, Ordinary and Partial DEs, 2006 Springer Science + Business Media, LLC (2009).
[10] Susan C. Brenner, L. Ridgway Scott, The mathematical theory of finite element methods (3rd edition), 2008 Springer Sciences + Business Media, LLC.
Cite This Article
  • APA Style

    Benyam Mebrate, Purnachandra Rao Koya. (2015). Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions. American Journal of Applied Mathematics, 3(6), 297-304. https://doi.org/10.11648/j.ajam.20150306.19

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    ACS Style

    Benyam Mebrate; Purnachandra Rao Koya. Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions. Am. J. Appl. Math. 2015, 3(6), 297-304. doi: 10.11648/j.ajam.20150306.19

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    AMA Style

    Benyam Mebrate, Purnachandra Rao Koya. Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions. Am J Appl Math. 2015;3(6):297-304. doi: 10.11648/j.ajam.20150306.19

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  • @article{10.11648/j.ajam.20150306.19,
      author = {Benyam Mebrate and Purnachandra Rao Koya},
      title = {Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions},
      journal = {American Journal of Applied Mathematics},
      volume = {3},
      number = {6},
      pages = {297-304},
      doi = {10.11648/j.ajam.20150306.19},
      url = {https://doi.org/10.11648/j.ajam.20150306.19},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150306.19},
      abstract = {In this paper we have introduced Numerical techniques to solve a two dimensional Poisson equation together with Dirichlet boundary conditions. Specifically two methods are used for the purpose of numerical solution, viz. Finite difference method and Finite element method. The implementation of the solutions is done using Microsoft Office Excel worksheet or spreadsheet. The numerical solutions obtained by these two methods are also compared with each other graphically in two and three dimension.},
     year = {2015}
    }
    

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    T1  - Numerical Solution of a Two Dimensional Poisson Equation with Dirichlet Boundary Conditions
    AU  - Benyam Mebrate
    AU  - Purnachandra Rao Koya
    Y1  - 2015/12/14
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    N1  - https://doi.org/10.11648/j.ajam.20150306.19
    DO  - 10.11648/j.ajam.20150306.19
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
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    EP  - 304
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ajam.20150306.19
    AB  - In this paper we have introduced Numerical techniques to solve a two dimensional Poisson equation together with Dirichlet boundary conditions. Specifically two methods are used for the purpose of numerical solution, viz. Finite difference method and Finite element method. The implementation of the solutions is done using Microsoft Office Excel worksheet or spreadsheet. The numerical solutions obtained by these two methods are also compared with each other graphically in two and three dimension.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

  • School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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