Advertisement

Analytic Method for Solving Heat and Heat-Like Equations with Classical and Non Local Boundary Conditions

  • Ahmed Cheniguel
Chapter

Abstract

In this paper, heat and heat-like equations with classical and non local boundary conditions are presented and a homotopy perturbation method (HPM) is utilized for solving the problems. The obtained results as compared with previous works are highly accurate. Also HPM provides continuous solutions in contrast to traditional methods, like finite difference method, which only provides discrete approximations. It is found that this method is a powerful mathematical tool and can be applied to a large class of linear and non linear problems in different fields of science and technology.

Keywords

Diffusion equation Exact solution Heat-like equation Homotopy perturbation method Initial boundary value problems Non local boundary conditions Partial differential equations 

References

  1. 1.
    A. Cheniguel, Numerical method for the heat equation with Dirichlet and Neumann boundary conditions, in Proceedings of the International Multi-Conference and Computer Scientists 2014, vol I, 12–14 Mar 2014, (IMECS, Hong Kong, 2014), pp. 535–539Google Scholar
  2. 2.
    A. Cheniguel, Numerical method for solving wave equation with non local boundary conditions. Lect. Notes Eng. Comput. Sci. 2203(1), 1190–1193 (2013)Google Scholar
  3. 3.
    A. Cheniguel, M. Reghioua, On the numerical solution of three-dimensional diffusion equation with an integral condition, in Proceedings of the World Congress on Engineering and Computer Science 2013, vol II, 21–23 Oct 2013 (WCECS, San Francisco, 2013), pp. 1017–1021Google Scholar
  4. 4.
    A. Cheniguel, Numerical method for solving heat equation with derivative boundary conditions. Lect. Notes Eng. Comput. Sci. 2194(1), 983–985 (2011)Google Scholar
  5. 5.
    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
  6. 6.
    A. Cheniguel, A. Ayadi, Numerical method for non local problem. Sci. Technol. A-N30, 15–18 (2009)Google Scholar
  7. 7.
    S. Momani, Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method. Appl. Math. Comput. 165(2), 459–472 (2005)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    G. Ekolin, Finite difference methods for a non local boundary value problem for the heat equation. BIT 31, 245–261 (1991)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    G. Adomian, A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135, 501–544 (1988)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    J.H. He, A coupling method of homotopy technique for non linear problems. Int. J. Non Linear Mech. 35, 37–43 (2000)CrossRefMATHGoogle Scholar
  11. 11.
    J.H. He, Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350, 87–88 (2006)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Damrongsak et al, Deferred correction technique to construct high-order schemes for the heat equation with Dirichlet and Neumann boundary conditions. Eng. Lett. 21(2), 61–67 (2013) Google Scholar
  13. 13.
    J.H. He, Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178(3/4), 257–262 (1999)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of SciencesKasdi Merbah University OuarglaOuarglaAlgeria

Personalised recommendations