IJSER Home >> Journal >> IJSER
International Journal of Scientific and Engineering Research
ISSN Online 2229-5518
ISSN Print: 2229-5518 9    
Website: http://www.ijser.org
scirp IJSER >> Volume 2, Issue 9, September 2011
Comparison of Variational Iteration Decomposition Method with Optimal Homotopy Asymptotic of 12th Order Boundary Value Problems
Full Text(PDF, 3000)  PP.  
Mukesh Grover, Dr. Arun Kumar Tomer
Twelfth order boundary value problems, Approximate analytical solution, Variational Iteration Decomposition Method, optimal homotopy Asymptotic method, Ordinary Differential Equations, Error Estimates
In this work, we consider special problem consisting of twelfth order two-point boundary value by using the Optimal Homotopy Asymptotic Method and Variational Iteration Decomposition Method. Now, we discuss the comparison in between Optimal Homotopy Asymptotic Method and Variational Iteration Decomposition Method. These proposed methods have been thoroughly tested on problems of all kinds and shows very accurate results. A numerical example is present and approximate is compared with exact solution and the error is compared with Optimal Homotopy Asymptotic Method and Variational Iteration Decomposition Method to assess the efficiency of the Optimal Homotopy Asymptotic Method at 12th order Boundary values problems.
[1] Adomian, G., 1991. A review of the decomposition method and some recent results for Nonlinear equations. Comput. Math. Appl., 101-127.

[2] He, J.H. (2004). The Homotopy Perturbation Method for Non- Linear Oscillators with Discontinuities. Applied Maths. Computer. 287 –292.

[3] He, J.-H., 2003. Variational approach to the sixth order boundary value problems. Applied Math. Computer, 537-538.

[4] Wazwaz, A.M., 2000. Approximate solutions to boundary value problems of higher- order By the modified decompositionmethod.Computer.Math.Appl.679-691

[5] Siddique, S.S. and E.H. Twizell, 1997. Spline solutions of linear twelfth-order boundary Value Problems Computer Math. Appl., 371-390.

[6] Siddique, S.S. and Ghazala Akram, 2008. Solutions of 12th order boundary value problems Using non-polynomial spline technique. Appl. Math.Comput.,559-571.

[7] He, J.-H., 2006. Homotopy perturbation methodfor solving boundary value problems.87-88.

[8] Ghotbi, Abdoul R., Barari, A. and Ganji, D. D, (2008). Solving Ratio-Dependent Predator- Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method. Math. Prob.Eng., 1-8.

[9] Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford, Reprinted: Dover Books, New York, 1981.

[10] Marinca, V., N. Herisanu and I. Nemes, 2008.Optimal homotopy asymptotic method with Application to thin film flow. Cent. Eur. J. Phys. 648-653.

[11] Ghasemi, M., Tavassoli Kajani,M. and Babolian, E. (2007). Numerical Solution of the Nonlinear Volterra–Fredholm Integral Equations by using Homotopy Perturbation Method. Appl. Math. Computer 446-449.

[12] Marinca, V. and N. Herisanu, 2008. An optimal homotopy asymptotic method for solving Nonlinear equations arising in heat transfer. Int. Comm. Heat and Mass Tran. 710-715.

[13] S. H. Mirmoradi, S. Ghanbarpour, I. Hosseinpour, A. Barari, (2009). Application of Homotopy perturbation method and variational iteration method to a nonlinear fourth order Boundary value problem. Int. J.Math.Analysis., 1111-1119.

[14] Marinca, V., N. Herisanu, C. Bota and B. Marinca,2009. An optimal homotopy asymptoticMethod applied to the steady flow of fourth-grade fluid pasta porous plate. App.Math.245-51

[15] Islam, S.-U., S. Haq and J. Ali, 2009. Numerical solution of special 12th-order boundaryValue Problems using differential transform method. Comm. Nonl. Sc. Nu. Sim.1132-1138.

[16] J.H. He. Variational iteration method, a kind of non-linear analytical techniques, some Examples inter. j. Nonlinear Mech., (1999):699-708

[17] J.H. He. Variational iteration method, new development and applications, Computer math.Appl.54 (2007):881-894

[18] J.H. He. Variational iteration method, some resent results and new interpretations. J. Computer math.Appl.54 (2007):881- 894

[19] J.H. He. Variational iteration method, a kind of non-linear analytical techniques, some Examples inter. j. Nonlinear Mech., (1999):699-708

[20] M.A. Noor , S.T. Mohyud-Din: a new approach to solving fifth order Boundary value Problems. , inter. j. Nonlinear Science,(2009):143-148

Untitled Page