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Variational Iteration Method for the Solution of Boundary Value Problems

Olayiwola M.O.; Gbolagade A .W.; Akinpelu F. O.

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

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  • Abulwafa E.M, Abdou M.A, Mahmoud A.A. "Nonlinear fluid flows in pipe-like domain problems using VIM "soliton and fractals 32(4) pp. 1384-1397,2007.
  • Abulwafa E.M, Abdou M.A, Mahmoud A.A. "The solution of nonlinear coagulation problem with mass " soliton and Fractals. 29 (2) 313-330, 2006.
  • Barari A et al. "An approximate solution for boundary value problems in structural Engineering and Fluid Mechanics." Mathematical problems in Engineering. 2008
  • Batiha B. et al "Application of Variational Iterational method to a General Riccati Equation". Int. Mathematical Forum, 2, no 56, 2759- 2770, 2007.
  • Biazar J., Ghazuini H. "He-s Variatonal iteration method for solving linear and non-linear system of ordinary differential equations". Applied Maths and Computation 191, 281-287, 2007.
  • Bildik N., Konuralp A. "The use of variation iteration method, differential transform method and Adomain decomposition method for solving different types of nonlinear pole". Int. J. nonlinear Science; Numerical Simulation 7(1) 65-70, 2006.
  • Celik E et al. "Numerical method to solve chemical differential Allgerai equation." Int. J. of Quantum chemistry, 89(5), 447-451, 2002.
  • Diethelin K. and Ford N.J. "Analysis of fractional differential equation". J. math and Appl. 265 229-248, 2002.
  • Djidjeli K. et al "Numerical methods for special nonlinear boundary value problems of order 2m". J. of Computational and Appl. Mathematics Vol. 47, no 1, 161-169, 2006. [10] Draganescu G E, capalnasan V. "Nonlinear relaxation phenomenon in polycrystalline solid" int. J nonlinear Numerical Simulation 4(3) 219- 225, 2003. [11] Ganji D.D. et al. "A Comparison of Variational iteration method with Adomain decomposition method in some highly nonlinear equations". International Journal of Science and Technology Vol. 2, No 2, 179-188, 2007. [12] He. J.H "Approximate analytical solution for seepage flow with fractional derivatives in porous media". Compt. Math. App. Mech. Eng. 167. 57-68, 1998. [13] He. J.H "Approximate solution of nonlinear differential equations with convolution product nonlinearities" Comp. Math. Apply Mech. Eng. 167: 69-73. 1998. [14] He. J.H "Variational iteration method for autonomous ordinary differential system." App. Math and Computation, 114:115-123, 2000. [15] Inokuti M. et al." General use of the Lagrange multipleiire in nonlinear mathematical physics in: S." Nemat Nasser (Ed), Vanational method in the mechanics of solid, Pergamon Press, 156-162, 1978. [16] Ji-Huan He "Variational iteration methods some recent results and new interpretation." J. of competition and Applied mathematics 207 3-17, 2007. [17] Ji-Huan He. "Variational Iteration method: a kind of non-linear analytical technique: Some examples." Int. Journal of Non-linear mechanics (3494) 699-708, 1999. [18] Levant Yilmaz "Some Considerations on the series solution of Differential equations and its engineering Applications." RMZ Materials and Geo-environment, Vol. 53, No 1, 247-259, 2006. [19] Lu J.F. "variational Iteration method for solving two-point boundary value problems. " Journal of computational and Applied Mathematics 207(1) 92-95, 2007. [20] Ma T.F and Silva J. Da "Iterative solution for a beam equation with nonlinear boundary conditions of third order", Applied mathematics and Computation, Vol. 159 no 1. 11-18, 2004. [21] Muhammed A.N, Syed T.M "Variational Iteration Decomposition method for solving Eight-Order Boundary Value Problem." Diff. Equation and Nonlinear mechanics. Vol. Id 19529, 2007. [22] Nuran Guzek, Bayram M. "Power Series solution of nonlinear first order differential equations systems" Trakya Univ. J.Se, 6(1). 107-111, 2005. [23] Odibat Z.M, Momani S. "Application of Variation iteration method to nonlinear differential equation of fractional order". Int. J to Nonlinear Science. Numerical Simulation 7(1) 27-34, 2006. [24] Olayiwola M.O et al (2008): on the existence of solution of differential equation of fractional order. J. of Modern Maths. and Statistics 2(5) 157- 159. [25] Olayiwola M.O, Gbolagade A.W. "On the Chaotic behavoiour of Hamonically driven Oscillator". Far East J. of Dynamical Systems Vol. 10, Issue 1, 47-52, 2008. [26] Podhibny I. "Fractional Differential equations" Academic Press, San Diego, 1999. [27] Saharay S... Bera R.K. "Solution of an extraordinary differential equation by Adomain decomposition method." J. of Applied Maths 4, 331-338, 2004. [28] Siddiqi S.S. Twizell. E.H. "Spline solution of linear eight-order boundary value problems." Computer methods in Apply Mechanics and engineering Vol. 131, no 3-4, 309-325, 1996. [29] Tatari M, Delighan M. "on the convergence of He-s Variational iteration method" Journal of computational and applied Mathematics 207 (1) 121-128, 2007. [30] Wazwaz A M. "A reliable algorithm for obtaining positive solution for nonlinear boundary value problems". Computer Math App 41(10-11) 1237-1244, 2001. [31] Wei-Xia Qian et al. "He-s Iteration Formulation for solving Nonlinear Algebraic equations." Journal of Physics: Conference series 96 1-6, 2008.
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