Modified Variational Iteration Method with Chebyshev Polynomials for Solving 12th order Boundary Value problems

Jonathan Tsetimi*    -  Department of Mathematics, Delta State University, Abraka, Nigeria
Ogeh K.O  -  Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin, Nigeria
Disu A. B  -  National Open University of Nigeria, Nigeria

(*) Corresponding Author
DOI: 10.21580/jnsmr.2022.8.1.2693

We consider in this paper an illustration of the modified variational iteration method (MVIM) as an effective and accurate solver of 12th order boundary value problem (BVP). For this reason, the Chebyshev polynomials of the principal kind was utilized as a premise capabilities in the guess of the logical capability of the given issue. The strategy is applied in an immediate manner without utilizing linearization or irritation. The subsequent mathematical confirmations recommend that the strategy is without a doubt successful and exact as applied to a few direct and nonlinear issues as mathematical trial and error. Maple 18 was used for all computational simulations carried out in this research.

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Keywords: Boundary value problems; Chebyshev polynomials of the first kind; variational iteration method; basis functions

  1. M.M. Khader, “Introducing an Efficient Modification of the Variational Iteration Method by Using Chebyshev Polynomial,” Applications and Applied Mathematics: An International Journal (AAM), 7:283-299, 2012.
  2. S.A. Ojobor S.A, and K.O. Ogeh, "Modified Variational Iteration Method for Solving Eight Order Boundary Value Problem using Canonical Polynomials," Transactions of Nigerian Association of Mathematical Physics, 4:45-50, 2017.
  3. I.N. Njoseh I.N and E.J. Mamadu, "The numerical solution of fifth-order boundary value problems using Mamadu-Njoseh polynomials", Science World Journal, 11(4):21-24, 2016a.
  4. I.N. Njoseh, and E.J. Mamadu, "Numerical Solutions of a Generalized Nth Order Boundary Value Problems using Power Series Approximation Method," Applied Mathematics, 7:1215-1224, 2016b.
  5. E.J. Mamadu, and I.N. Njoseh, "Tau-Collocation Approximation Approach for Solving First and Second Order Ordinary Differential Equations," Journal of Applied Mathematics and Physics, 4: 383-390, 2016.
  6. M.A. Noor, and S.T. Mohyud-Din, "A New approach for solving Fifth Order Boundary Value Problem," International Journal of Nonlinear Science, 9:387-393, 2010a.
  7. M.A. Noor, and S.T. Mohyud-Din, "Variational Decomposition Method for Solving Sixth Order Boundary Value Problems," Journal of Applied Maths & Informatics, 27(5-6):1343-1359, 2007b.
  8. M.A. Noor, and S.T. Mohyud-Din, "Variational Iteration Decomposition Method for Solving Eight Order Boundary Value Problem, Differential Equation and Nonlinear Mechanic", 2007c.
  9. M.A. Noor, and S.T. Mohyud-Din,"Variational Iteration Method for Fifth Order Boundary Value Problem using He’s Polynomials," Mathematical Methods in Engineering, Article ID 954794, 12 pages, doi:10.1155/2008/954794, 2007d.
  10. S.T. Mohyud-Din, M.A. Noor, and K.I. Noor, "Approximate Solutions of Twelfth-order Boundary Value Problems," Journal of Applied Mathematics, Statistics and Informatics, 4:139-152, 2008.
  11. H. Mirmoradi, H. Mazaheripour, S. Ghanbarpour and S. Barari, "Homotopy Perturbation Method for solving twelfth order boundary value problem," International journal of Research and review in Applied Science, 1(2):164-173, 2009.
  12. S.T. Mohyud-Din, and A. Yildirim, "Solutions of Tenth and Ninth-Order Boundary Value Problems by Modified Variational Iteration Method," Application and applied mathematics, 5(1):11 – 25, 2010.
  13. A. Fazal-i-Haq Arshed and I. Hussain, "Solution of sixth-order boundary value problems by Collocation method," International Journal of Physical Sciences, 7(43):5729-5735, 2012.
  14. S.S . Shahid, and M. Iftikhar, "Variational Iteration Method for solution of Seventh Order Boundary Value Problem using He’s Polynomials," Journal of the Association of Arab Universities for Basic and Applied Sciences,18: 60–65, 2015.
  15. H.N. Caglar, S.H. Caglar, and E.H. Twizellll, "The numerical solution of fifth-order value problems with sixth degree B-spline function," Applied Mathematics Letters, 12(5):25-30, 1999.
  16. G. Adomian, "A review of the decomposition method and some recent results for nonlinear equation," Math. Computer Modeling, 13(7):17-43, 1990.
  17. E. Hesameddini, A. Rahimi, " A New Modification of the Reconstruction of
  18. Variational Iteration Method for Solving Multi-order Fractional Defferential Equations," Journal of Sciences, Islamic Republic of Iran, 27(1):79-86 ,2016.
  19. W.Abbas, M.Fathy, M. Mostafa, and A.M.A Heshem, "Galerkin Method for Nonlinear Higher-Order Boundary Value Problems Based on Chebyshev Polynomials," Journal of Physics :Conference Series, 2128:1-7 2021.
  20. Elsgolts, L. “Differential Equations and the Calculus of Variations”, translated from the Russian by G. Yankovsky, Mir, Moscow. 1977.
  21. Bell, W.W. "Special Functions for Scientist and Engineers", New York Toronto Melbourne, 2005.

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