Advertisement

One Dimensional Heat Flow

  • Abdul-Majid Wazwaz
Part of the Nonlinear Physical Science book series (NPS)

Abstract

In Chapter 1, it was indicated that many phenomena of physics and engineering are expressed by partial differential equations PDEs. The PDE is termed a Boundary Value Problem (BVP) if the boundary conditions of the dependent variable u and some of its partial derivatives are often prescribed. However, the PDE is called an Initial Value Problem (IVP) if the initial conditions of the dependent variable u are prescribed at the starting time t=0. Moreover, the PDE is termed Initial-Boundary Value Problem (IBVP) if both initial conditions and boundary conditions are prescribed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).zbMATHGoogle Scholar
  2. 2.
    G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Modelling, 13(7), 17–43, (1992).CrossRefMathSciNetGoogle Scholar
  3. 3.
    S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover, New York, (1993).zbMATHGoogle Scholar
  4. 4.
    J.H. He, A variational iteration method-a kind of nonlinear analytical technique: Some examples, Int. J. Nonlinear Mech., 34, 699–708, (1999).zbMATHCrossRefGoogle Scholar
  5. 5.
    J.H. He, Variational iteration method: some recent results and new interpretations, J. Comput. and Appl. Math., 207(1), 3–17, (2007).zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    F. John, Partial Differential Equations, Springer-Verlag, New York, (1982)Google Scholar
  7. 7.
    A.M. Wazwaz, A reliable modification of Adomian’s decomposition method, Appl. Math. and Comput., 92(1), 1–7, (1998).zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema Publishers, The Netherlands, (2002).zbMATHGoogle Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abdul-Majid Wazwaz
    • 1
  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

Personalised recommendations