IJSER Home >> Journal >> IJSER
International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 10    
Website: http://www.ijser.org
scirp IJSER >> Volume 2, Issue 10, October 2011 Edition
Modified Variational Iteration Method for the Solution of nonlinear Partial Differential Equations
Full Text(PDF, 3000)  PP.  
Author(s)
Olayiwola , M. O Akinpelu, F. O , Gbolagade, A .W
KEYWORDS
variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation, modified variational iteration method, correction functional.
ABSTRACT
The Variational Iteration Method (VIM) has been shown to solve effectively, easily and accurately a large class of linear and nonlinear problems with approximations converging rapidly to exact solutions. We present a new Modified Variational Iteration Method (MVIM) for the solution of some partial differential equations of physical significance.
References
[1] Abulwafa E.M, Abdou M.A, Mahmoud A.A, “ Nonlinear fluid flows in pipe-like domain problems using VIM class”, Soliton And Fractals 2007, 32(4) 1384-1397.

[2] Abulwafa E.M, Abdou M.A, Mahmoud A.A. “ The solution of nonlinear coagulation problem with mass class”, Soliton and Fractals. 2006,29 (2) 313-330.

[3] Awodola T. O.” Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load”. Journal of Mathematics and Statistics 3 (4): 228-232, 2007

[4] Barari A “ An approximate solution for boundary value problems in structural Engineering and Fluid Mechanics”. Mathematical problems in Engineering. 2008

[5] Batiha B. “Application of Variational Iterational method to a General Riccat Equation”. Int. Mathematical Forum, 2, 2007, no 56, 2759-2770.

[6] Biazar J., Ghazuini H, “He’s Variatonal iteration method for solving linear and non-linear system of ordinary differential equations”. Applied Maths and Computation 2007, 191, 281-287.

[7] 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 2006,7(1) 65-70.

[8] Celik E “ Numerical method to solve chemical differential Allgerai equation”. Int. J. of Quantum chemistry, 2002,89(5), 447-451,.

[9] Diethelin K. and Ford N.J, “Analysis of fractional differential equation”. J. math and Appl.2002, 265 229-248.

[10] Djidjeli K. “Numerical methods for special nonlinear boundary value problems of order 2m”. J. of Computational and Appl. Mathematics Vol. 47, 2006,no 1, 161-169,.

[11] Dogan Kaya. “The use of Adomian decomposition method for solving a specific nonlinear partial differential equations”. Bull. Beg. Maths. Soc. 9(2002), 343-349.

[12] Draganescu G E, capalnasan V. “Nonlinear relaxation phenomenon in polycrystalline solid” int. J nonlinear Numerical Simulation 4(3) 219-225.

[13] Ganji D.D. “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, 2007,179-188.

[14] Gbadeyan, J A& S.T Oni , “Dynamics behavior of beam and rectangular plates under moving loads.” Journal of Sound and Vibration 1995,199,33-50.

[15] He. J.H “Approximate analytical solution for seepage flow with fractional derivatives in porous media”. Compt. Math. App. Mech. Eng. 167. 1998 57-68.

[16] He. J.H “Approximate solution of nonlinear differential equations with convolution product nonlinearities” Comp. Math. Apply Mech. Eng. 167: 199869-73.

[17] He. J.H “Variational iteration method for autonomous ordinary differential system.” App. Math and Computation, 2000; 114:115-123.

[18] Hossein Jafari etal “Application of Homotopy Perturbation Method for Solving Gas Dynamic Equation”. Applied Mathematical Sciences, Vol.2,2008. No 48,2393-2396.

[19] Jemal Peradze “ A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam”. Journal of Applied MathematicsVolume 2009,

[20] Inokuti M. et al. (1978): General use of the Lagrange multiplier in nonlinear mathematical physics in: S. Nemat Nasser (Ed), Vanational method in the mechanics of solid, Pergamon Press, 156-162.

[21] Ji-Huan He (2007): Variational iteration methods some recent results and new interpretation. J. of competition and Applied martherates 207 3-17.

[22] Ji-Huan He. (1999): Variational Iteration method: a kind of non-linear analytical technique: Some examples. Int. Journal of Non-linear mechanics 3494) 699-708.

[23] Levant Yilmaz “Some Considerations on the series solution of Differential equations and its engineering Applications.” RMZ Materials and Geo-environment, Vol. 53,2006, No 1, 247-259.

[24] Lu J.F. “Variational Iteration method for solving two-point boundary value problems.” Journal of computational and Applied Mathematics 2007(1) 92-95.

[25] 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 ,2004,no 1. 11-18.

[26] Muhammed A.N, Syed T.M ,”Variational Iteration Decomposition method for solving Eight-Order Boundary Value Problem.”Diff. Equation and Nonlinear mechanics. 2007 Vol. Id 19529.

[27] Nuran Guzek, Bayram M. , “Power Series solution of nonlinear first order differential equations systems” Trakya Univ. J.Se, 2005,6(1). 107-111.

[28] Odibat Z.M, Momani S. “Application of Variation iteration method to nonlinear differential equation of fractional order.” Int. J to Nonlinear Science. Numerical Simulation 2006,7(1) 27-34.

[29] Olayiwola M.O et al,”Application of modified power series method for the solution of system of differential equations”. Journal of Nigerian Association of Mathematical Physics Vol. 15, 2009,pp 91-94.

[30] Olayiwola M.O, Gbolagade A.W. “ On the Chaotic behavoiour of Hamonically driven Oscillator” Far East J. of Dynamical Systems Vol. 10, 2008, issue 1, 47-52.

[31] Podhibny I. “ Fractional Differential equations” Academic Press, 1999, San Diego,.

[32] Saharay S.. Bera R.K. “ Solution of an extraordinary differential equation by Adomain decomposition method”. J. of Applied Maths 4,2004, 331-338.

[33] Siddiqi S.S. Twizell. E.H. “ Spline solution of linear eight-order boundary value problems” Computer methods in Apply Mechanics and engineering Vol. 131, 1996,no 3-4, 309-325.

[34] Tatari M, Delighan M. “On the Convergence of He’s Variational iteration method” Journal of computational and applied Mathematics 2007 (1) 121-128.

[35] Wang . L and Ni. Q “ Vibration of Slender Structures Subjected to Axial Flow or Axially Towed in Quiescent Fluid” Advances in Acoustics and Vibration Volume 2009, Article ID 432340

[36] Wazwaz A M. “ A reliable algorithm for obtaining positive solution for nonlinear boundary value problems.” Compute Math App 41(10-11) 2001, 1237-1244.

[37] Wazwaz, A M. “Analytic treatment for variable cefficient fourth-order parabolic partial differential equations.” Appl math. Comput. 123: 2001, pp. 219-227

[38] Wazwaz, A. M. “ Partial differential equations, methods and applications.” A. A. Balkema Publishers

[39] Wei-Xia Qian “He’s Iteration Formulation for solving Nonlinear Algebraic equations.” Journal of Physics: Conference series 2008, 96 1-6.

[40] Yujun Cui, Yumei Zou “ Existence and Uniqueness of solutions for Fourth-Order Boundary-Value Problems in Banach Spaces.” Electronic Journal of Differential Equations, Vol. 2009(2009), No. 33, pp. 1–8

Untitled Page