Variational iteration method for solving sixth-order boundary value problems

Abstract In this paper, we have shown that sixth-order boundary value problems can be transformed into a system of integral equations, which can be solved by using variational iteration method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the method. It is observed that the proposed technique is more useful and is easier to implement because one does not need to calculate the Adomian’s polynomials which is itself a difficult task.

[1]  Y. Fung,et al.  Variational Methods in the Mechanics of Solids , 1982 .

[2]  Muhammad Aslam Noor,et al.  Homotopy perturbation method for solving sixth-order boundary value problems , 2008, Comput. Math. Appl..

[3]  Mohamed El-Gamel,et al.  Sinc-Galerkin method for solving linear sixth-order boundary-value problems , 2004, Math. Comput..

[4]  H. Sekine,et al.  General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics1 , 1980 .

[5]  E. H. Twizell,et al.  Numerical methods for the solution of special and general sixth-order boundary-value problems, with applications to Bénard layer eigenvalue problems , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[6]  Muhammad Aslam Noor,et al.  Modified Variational Iteration Method for Heat and Wave-Like Equations , 2008 .

[7]  Muhammad Aslam Noor,et al.  An efficient method for fourth-order boundary value problems , 2007, Comput. Math. Appl..

[8]  M. M. Chawla,et al.  Finite difference methods for two-point boundary value problems involving high order differential equations , 1979 .

[9]  P. Baldwin,et al.  Localised instability in a bénard layer , 1987 .

[10]  Muhammad Aslam Noor,et al.  Variational Iteration Method for Solving Initial and Boundary Value Problems of Bratu-type , 2008 .

[11]  Juri Toomre,et al.  Stellar convection theory. II - Single-mode study of the second convection zone in an A-type star , 1976 .

[12]  Edward H. Twizell,et al.  Spline solutions of linear sixth-order boundary-value problems , 1996, Int. J. Comput. Math..

[13]  E. H. Twizell Numerical Methods for Sixth-Order Boundary Value Problems , 1988 .

[14]  Giuseppe Saccomandi,et al.  New results for convergence of Adomian's method applied to integral equations , 1992 .

[15]  Muhammad Aslam Noor,et al.  Variational iteration technique for solving higher order boundary value problems , 2007, Appl. Math. Comput..

[16]  P. Baldwin,et al.  Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integral methods , 1987, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[17]  Abdul-Majid Wazwaz,et al.  The numerical solution of sixth-order boundary value problems by the modified decomposition method , 2001, Appl. Math. Comput..

[18]  Shahid S. Siddiqi,et al.  Solutions of 12th order boundary value problems using non-polynomial spline technique , 2006, Appl. Math. Comput..

[19]  S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability , 1961 .

[20]  Gary A. Glatzmaier,et al.  Numerical simulations of stellar convective dynamos III. At the base of the convection zone , 1985 .

[21]  Ravi P. Agarwal,et al.  Boundary value problems for higher order differential equations , 1986 .

[22]  Edward H. Twizell,et al.  Numerical methods for the solution of special sixth-order boundary-value problems , 1992 .