Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

FUNCTIONAL ITERATIVE METHODS FOR SOLVING TWO-POINT BOUNDARY VALUE PROBLEMS

  • Lim, Hyo Jin (Department of Mathematics, Chungbuk National University) ;
  • Kim, Kyoum Sun (Department of Mathematics, Chungbuk National University) ;
  • Yun, Jae Heon (Department of Mathematics, College of Natural Sciences, Chungbuk National University)
  • Received : 2013.01.21
  • Accepted : 2013.04.23
  • Published : 2013.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we first propose a new technique of the functional iterative methods VIM (Variational iteration method) and NHPM (New homotopy perturbation method) for solving two-point boundary value problems, and then we compare their numerical results with those of the finite difference method (FDM).

Keywords

References

  1. G. Adomain, New approach to nonlinear partial differential equations, J. Math. Anal. Appl. 102 (1984), 420-434 https://doi.org/10.1016/0022-247X(84)90182-3
  2. G. Adomian, M. Elrod and R. Rach, A new approach to boundary value equations and application to a generalization of Airy's equation, J. Math. Anal. Appl. 140 (1989), 554-568. https://doi.org/10.1016/0022-247X(89)90083-8
  3. A.H.A. Ali and K.R. Raslan, Variational iteration method for solving partial differential equations with variable coefficients, Chaos Soli. Frac. 40 (2009), 1520-1529. https://doi.org/10.1016/j.chaos.2007.09.031
  4. H. Aminikhah and J. Biazar, A New HPM for ordinary differential equations, Numer Methods Partial Differential Eq. 26 (2010), 480-489.
  5. J. Biazar and H. Ghazvini, He's variational iteration method for solving linear and nonlinear system of ordinary differential equations , Appl. Math. Comput. 191 (2007), 287-297. https://doi.org/10.1016/j.amc.2007.02.153
  6. J.H. He, Variational iteration method, a kine of non-linear analytical technique, Int. J. Nonlinear Mech. 34 (1999) 699-708. https://doi.org/10.1016/S0020-7462(98)00048-1
  7. J.H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng. 178 (1999), 257-262. https://doi.org/10.1016/S0045-7825(99)00018-3
  8. J.H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (2003) 74-79.
  9. J.H. He, The homotopy perturbation method nonlinear oscillators with discontinuities, Appl. Math. Comput. 151 (2004), 287-292. https://doi.org/10.1016/S0096-3003(03)00341-2
  10. J.H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput. 156 (2004) 527-539. https://doi.org/10.1016/j.amc.2003.08.008
  11. J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Soiltons Fractals 26 (2005) 695-700. https://doi.org/10.1016/j.chaos.2005.03.006
  12. J.H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A 350 (2006), 87-88. https://doi.org/10.1016/j.physleta.2005.10.005
  13. J.H. He, Variational iteration method: new development and applications, Comp. Math. Appl. 54 (2007) 881-894. https://doi.org/10.1016/j.camwa.2006.12.083
  14. J.H. He, Variational iteration method - some recent results and new interpretations, J. Comp. Appl. Math. 207 (2007) 3-17. https://doi.org/10.1016/j.cam.2006.07.009
  15. K.S. Kim and H.J. Lim, New homotopy perturbation method for solving integro-differential equations, J. Appl. Math. & Informatics 30 (2012) 699-717.
  16. J. Lu, Variational iteration method for solving two-point boundary value problems, J. Comput. Appl. Math. 207 (2007), 92-95. https://doi.org/10.1016/j.cam.2006.07.014
  17. R.S. Varga, Matrix iterative analysis, Springer-Verlag, Berlin, (2009).