Variational iteration method for solving sixth-order boundary value problems

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 6, 2009, Pages 2571-2580

  Noor, Muhammad Aslam ^a   Noor, Khalida Inayat ^a   Mohyud Din, Syed Tauseef ^a  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

Author keywords

Boundary value problems; Integral equations; Nonlinear problems; Variational iteration

Indexed keywords

BOUNDARY VALUE PROBLEMS; ITERATIVE METHODS; NONLINEAR EQUATIONS;

ADOMIAN POLYNOMIALS; ANALYTICAL RESULTS; BOUNDARY-VALUE PROBLEM; COMPUTABLE COMPONENTS; CONVERGENT SERIES; NONLINEAR PROBLEMS; ORDER BOUNDARIES; SYSTEM OF INTEGRAL EQUATIONS; VARIATIONAL ITERATION; VARIATIONAL ITERATION METHOD;

INTEGRAL EQUATIONS;

EID: 58349089715     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2008.10.013     Document Type: Article

References (22)

1. Agarwal R.P. Boundary value problems for higher-order differential equations (1986), World Scientific, Singapore
2. Akram G., and Siddiqi S.S. Solution of sixth order boundary value problems using non-polynomial spline technique. Appl Math Comput (2006)
3. Baldwin P. Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integral methods. Philos Trans Roy Soc Lond A 322 (1987) 281-305
4. Baldwin P. A localized instability in a Benard layer. Appl Anal 24 (1987) 1127-1156
5. Boutayeb A., and H Twizell E. Numerical methods for the solution of special sixth-order boundary value problems. Int J Comput Math 45 (1992) 207-233
6. Chawla M.M., and Katti C.P. Finite difference methods for two-point boundary-value problems involving higher order differential equations. BIT 19 (1979) 27-33
7. Chandrasekhar S. Hydrodynamics and hydromagnetic stability (1981), Dover, New York
8. Cherrauault Y., and Saccomandi G. Some new results for convergence of Adomian method applied to integral equations. Math Comput Model 16 2 (1992) 85-93
9. Gamel M.E., Cannon J.R., and Zayed A.I. Sinc-Galerkin method for solving linear sixth order boundary value problems. Appl Math Comput 73 (2003) 1325-1343
10. Glatzmaier G.A. Numerical simulations of stellar convection dynamics at the base of the convection zone. Fluid Dyn 31 (1985) 137-150
11. Aslam Noor M, Mohydu-Din ST. Modified variational iteration method for heat and wave-like equations. Act Appl Math (2008), doi:10.1007/S12190.008.0081.0.
12. Aslam Noor M., and Mohydu-Din S.T. Variational iteration method for solving initial and boundary value problems of Bratu-type, applications. Appl Math 3 (2008) 89-99
13. Inokuti M., Sekine H., and Mura T. General use of the Lagrange multiplier in nonlinear mathematical physics. Variational methods in the mechanics of solids (1978), Pergamon Press, New York 156-162
14. Momani S, Aslam Noor M, Mohyud-Din ST. Numerical methods for solving a special sixth-order boundary value problem, preprint (2007).
15. Aslam Noor M., and Mohyud-Din S.T. An efficient method for fourth-order boundary value problems. Comput Math Appl 54 (2007) 1101-1111
16. Aslam Noor M., and Mohyud-Din S.T. Variational iteration technique for solving higher order boundary value problems. Appl Math Comput 189 (2007) 1929-1942
17. Aslam Noor M., and Mohyud-Din S.T. Homotopy perturbation method for solving sixth order boundary value problems. Comput Math Appl 55 (2008) 2953-2972
18. Siddiqi S.S., and Twizell E.H. Spline solutions of linear sixth-order boundary value problems. Int J Comput Math 60 (1996) 295-304
19. Toomore J., Zahn J.P., Latour J., and Spiegel E.A. Stellar convection theory II: single-mode study of the secong convection zone in A-type stars. Astrophys J 207 (1976) 545-563
20. Twizell E.H., and Boutayeb A. Numerical methods for the solution of special and general sixth-order boundary value problems, with applications to Benard layer eigenvalue problem. Proc Roy Soc Lond 431 (1990) 433-450
21. Twizell E.H. Numerical methods for sixth-order boundary value problems. Numerical mathematics, Singapore, international series of numerical mathematics vol. 86 (1988), Birkhauser, Basel 495-506
22. Wazwaz A.M. The numerical solution of sixth order boundary value problems by the modified decomposition method. Appl Math Comput 118 (2001) 311-325