Change in the form of fourth order two-point boundary value problem for solving by Adomian decomposition and homotopy perturbation methods

Document Type : Research Paper


1 Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

2 Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16315-1618, Tehran, Iran

3 Department of mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran


In this paper, we convert the fourth-order differential equations with two-point boundary conditions into a differential equation with homogeneous boundary conditions. Because the decomposition methods are closely related to the McLaren series, the McLaren series has a higher accuracy for points close to zero. Then we use Adomian decomposition and homotopy perturbation methods to solve three linear and nonlinear experiments.


[1] G. Akram and I.A. Aslam, Solution of fourth order three-point boundary value problem using ADM and RKM, J. Assoc. Arab Univ. Basic Appl. Sci. 20 (2016), 61–67.
[2] A. Aminataei and S.S. Hosseini, Comparison of Adomian decomposition and double decomposition methods for boundary-value problems, Euro. J. Sci. Res. 2 (2005), 48–56.
[3] E. Babolian, S.M. Hosseini and M. Heydari, Improving homotopy perturbation method with optimal Lagrange interpolation polynomials, Ain Shams Engin. J. 3 (2012) 305–311.
[4] M.G. Cui and F.Z. Geng, Solving singular two-point boundary value problem in reproducing kernel space, J. Comput. Appl. Math. 205 (2007), 6–15.
[5] F.Z. Geng and M.G. Cui, Solving singular nonlinear two-point boundary value problems in the reproducing kernel space, J. Korean Math. Soc. 45 (2008), 77–87.
[6] F.Z. Geng and M.G. Cui, Solving nonlinear multi-point boundary value problems by combining homotopy perturbation and variational iteration methods, Int. J. Nonlinear Sci.d Numer. Simul. 10 (2009), 597–600.
[7] F.Z. Geng and M.G. Cui, A novel method for nonlinear two-point boundary value problems: combination of ADM and RKM, Appl. Math. Comput. 217 (2011), 4676–4681.
[8] A. Ghazala and U.R. Hamood, Reproducing kernel method for fourth order singularly perturbed boundary value problems, World Appl. Sci. J. 16 (2012), 1799–1802.
[9] J.H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput. 156 (2004), 527–539.
[10] Y. Khan and Q. Wu, Homotopy perturbation transform method for nonlinear equations using He’s polynomials, Comput. Math. Appl. 61 (2011), 1963–1967.
[11] D.R. Kincaid, Numerical Analysis Mathematics of Scientific Computing, American Mathematical Soc., 1942.
[12] S.J. Liao, Boundary element method for general nonlinear differential operators, Eng. Anal. Boundary Ement. 20 (1997), 91–99.
[13] M. Mestrovic, The modified decomposition method for eighth order boundary value problems, Appl. Math. Comput. 188 (2007), 1437–1444.
[14] A.H. Nayfeh, Problems in Perturbation, John Wiley and Sons, New York, 1985.
[15] M.A. Noor and S.T. Mohyud-Din, An efficient method for fourth-order boundary value problems, Comput. Math. Appl. 54 (2007) 1101–1111.
[16] M. Sadaf and G. Akram, A Legendre-homotopy method for the solutions of higher order boundary value problems, J. King Saud Univ. Sci. 32 (2020), no. 1, 537–543.
[17] S.S. Siddiqi and A. Ghazala, Numerical solution of a system of fourth order boundary value problems using cubic non-polynomial spline method, Appl. Math. Comput. 190 (2007), 652–661.
[18] M. Tatari and M. Dehghan, The use of the Adomian decomposition method for solving multipoint boundary value problems, Phys. Scripta 73 (2006), 672–676.
[19] A.M. Wazwaz, The numerical solution of fifth-order boundary-value problems by Adomian decomposition, J. Comput. Appl. Math. 136 (2001), 259–270.
Volume 14, Issue 7
July 2023
Pages 255-260
  • Receive Date: 24 May 2022
  • Revise Date: 17 June 2022
  • Accept Date: 11 July 2022
  • First Publish Date: 03 December 2022