On the Numerical Solution of Multi-dimensional Diffusion Equation with Non Local Conditions

Conference paper

Abstract

In this paper, we investigate the solution of multi-dimensional diffusion equation using decomposition method. We consider two cases: a two-dimensional equation with non local boundary conditions and a three-dimensional equation with an integral condition. The method is reliable and gives a solution in a series form with high accuracy. It also guarantees considerable saving of calculation volume and time as compared to traditional methods. The obtained results show that the decomposition method is efficient and yields a solution in a closed form.

Keywords

Adomian decomposition method Diffusion equation Exact solution Integral condition Non local boundary conditions Partial differential equations 

References

  1. 1.
    A. Cheniguel, Numerical method for solving wave equation with non local boundary conditions, in Proceeding of the International Multi-Conference and Computer Scientists 2013, vol. II, pp. 1190–1193, IMECS 2013, , Hong Kong, 13–15 March 2013Google Scholar
  2. 2.
    A. Cheniguel, On the numerical solution of three-dimensional diffusion equation with an integral condition, in Lecture Notes in Engineering and Computer Science 2013, WCECS 2013, pp. 1017–1021, San Francisco, 23–25 Oct 2013Google Scholar
  3. 3.
    A. Cheniguel, Numerical simulation of two-dimensional diffusion equation with non local boundary conditions. Int. Math. Forum 7(50) 2457–2463 (2012)Google Scholar
  4. 4.
    A. Cheniguel, Numerical method for solving heat equation with derivative boundary conditions, in Proceedings of the World Congress on Engineering and Computer Science 2011, vol. II, pp. 983–985, WCECS 2011, San Francisco, 19–21 Oct 2011Google Scholar
  5. 5.
    A. Cheniguel, A. Ayadi, Solving heat equation by the adomian decomposition method, in Proceeding of the World Congress on Engineering 2011, vol. I, pp. 288–290, WCE 2011, London, 6–8 July 2011Google Scholar
  6. 6.
    A. Cheniguel, A. Ayadi, Solving non homogeneous heat equation by the adomian decomposition method. Int. J. Numer. Methods Appl. 4(2), 89–97 (2010)MATHGoogle Scholar
  7. 7.
    A. Cheniguel, Numerical method for non local problem, Int. Math. Forum 6(14),659–666 (2011)Google Scholar
  8. 8.
    M. Siddique, Numerical computation of two-dimensional diffusion equation with non local boundary conditions, IAENG Int. J. Appl. Math. 40(1) IJAM_401_04, 91–99 (2010)Google Scholar
  9. 9.
    M. Akram, A parallel algorithm for the heat equation with derivative boundary conditions. Int. Math. forum 2(12) 565–574 (2007)Google Scholar
  10. 10.
    A. Akram, M.A. Pasha, Numerical method for the heat equation with a non local boundary condition. Int. J. Inf. Syst. Sci. 1(2), 162–171 (2005)MATHMathSciNetGoogle Scholar
  11. 11.
    A.B. Gumel, W.T. Ang, F.H. Twizell, Efficient parallel algorithm for the two-dimensional dffusion equation subject to specification of mass. Inter. J. Comput. Math. 64, 153–163 (1997)Google Scholar
  12. 12.
    G. Adomian, Solving frontier problems of physics : the decomposition method (Kluver Academic Publishers, Dordrecht, 1994)MATHGoogle Scholar
  13. 13.
    B.J. Noye, K.J. Hayman, Explicit two level finite difference methods for two-dimensional diffusion equation. Inter. J. Comput. Math. 42 223–236 (1992)Google Scholar
  14. 14.
    G. Adomian, R. Rach, Noise terms in decomposition solution series. Comput. Math. Appl. 24(11), 61–64 (1992)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    G. Ekolin, Finite difference methods for a non local boundary value problem for the heat equation. BIT 31, 245–261 (1991)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    G. Adomian, A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135, 501–544 (1988)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Sciences, Department of Mathematics and Computer ScienceKasdi Merbah UniversityOuarglaAlgeria

Personalised recommendations