Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2008, Article ID 578723, 11 pages
http://dx.doi.org/10.1155/2008/578723
Research Article

Exact and Numerical Solutions of Poisson Equation for Electrostatic Potential Problems

Department of Electrical Education, Firat University, 23119 Elazig, Turkey

Received 19 September 2007; Accepted 17 March 2008

Academic Editor: Mohammad Younis

Copyright © 2008 Selçuk Yıldırım. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J.-H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, vol. 2 of CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC Press, Boca Raton, Fla, USA, 2004. View at Zentralblatt MATH · View at MathSciNet
  4. S. Abbasbandy, “Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 431–438, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-H. He, “The homotopy perturbation method nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. T. Öziş and A. Yildirim, “A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 243–248, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Öziş and A. Yildirim, “Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 239–242, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J.-H. He, “New interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Abbasbandy, “Application of He' homotopy perturbation method to functional integral equations,” Chaos, Solitons and Fractals, vol. 31, no. 5, pp. 1243–1247, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L.-N. Zhang and J.-H. He, “Homotopy perturbation method for the solution of the electrostatic potential differential equation,” Mathematical Problems in Engineering, vol. 2006, Article ID 83878, 6 pages pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  12. S. T. Mohyud-Din and M. A. Noor, “Homotopy perturbation method for solving fourth-order boundary value problems,” Mathematical Problems in Engineering, vol. 2007, Article ID 98602, 15 pages pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K. Al-Khaled, “Theory and computation in singular boundary value problems,” Chaos, Solitons and Fractals, vol. 33, no. 2, pp. 678–684, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. A. Brebbia and S. Walker, Boundary Element Techniques in Engineering, Newnes-Butterworths, London, UK, 1980. View at Zentralblatt MATH · View at MathSciNet
  15. P. K. Kythe, An Introduction to Boundary Element Method, CRC Press, Boca Raton, Fla, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  16. P. W. Partridge, C. A. Brebbia, and L. C. Wrobel, The Dual Reciprocity Boundary Element Method, International Series on Computational Engineering, Computational Mechanics and Elsevier Applied Science, Southampton, UK, 1992. View at Zentralblatt MATH · View at MathSciNet
  17. M. A. Noor and S. T. Mohyud-Din, “An efficient algorithm for solving fifth-order boundary value problems,” Mathematical and Computer Modelling, vol. 45, no. 7-8, pp. 954–964, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. A. Noor and S. T. Mohyud-Din, “Homotopy perturbation method for solving sixth-order boundary value problems,” Computers & Mathematics with Applications. In press. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. A. Noor and S. T. Mohyud-Din, “Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 2, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J.-H. He, “Comparison of homotopy perturbation method and homotopy analysis method,” Applied Mathematics and Computation, vol. 156, no. 2, pp. 527–539, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. P. Hunter and A. Pullan, FEM/BEM notes, Ph. D. thesis, Department of Engineering Science, University of Auckland, Auckland, New Zealand, 2001. View at Zentralblatt MATH · View at MathSciNet
  26. S. Yıldırım, The investigation of electric fields in high voltage systems using the boundary element method, Ph. D. thesis, Graduate School of Natural and Applied Science, Firat University, Elazig, Turkey, 1999. View at Zentralblatt MATH · View at MathSciNet