Variation of parameters method for solving sixth-order boundary value problems
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.
Abstract
In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.
참고문헌 (32)
- R. P. Agarwal, "Boundary Value Problems for Higher Order Differential Equations" (1986), world scientific
- G. Akram, "Solution of sixth order boundary value problems using non-polynomial spline technique", Appl. Math. Comput., 181(1), pp.708~720 (2006)
- P. Baldwin, "Asymptotic estimates of the eigenvalues of a sixth-order boundary-value problem obtained by using global phase-integral methods", Phil, Trans. Roy. Soc. Lond., A 322(1566), pp.281~305 (1987)
- P. Baldwin, "Localized instability in a Benard layer", Appl. Aal., 24(1), pp.117~156 (1987)
- A. Boutayeb, "Numerical methods for the solution of special sixth-order boundary value problems", Int. J. Comput. Math., 45, pp.207~233 (1992)
- S. Chandrasekhar, "Hydrodynamics and Hydromagntic Stability" (1981), Dover
- M. M. Chawla, "Finite difference methods for two-point boundary-value problems involving higher order differential equations", BIT, 19, pp.27~33 (1979)
- Y. Cherrauault, "Some new results for convergence of G. Adomian’s method applied to integral equations", Math. Comput. Modeling, 16(2), pp.85~93 (1992)
- M. E. Gamel, "Sinc-Galerkin method for solving linear sixth order boundary value problems", Appl. Math. Comput., 73, pp.1325~1343 (2003)
- G. A. Glatzmaier, "Numerical simulations of stellar convection dynamics at the base of the convection zone", geophysics. Fluid Dynamics, 31, pp.137~150 (1985)
- J. H. He, "Variational approach to the sixth order boundary value problems", Appl. Math. Comput., 143, pp.235~236 (2003)
- W. X. Ma, "Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions", Trans. Amer. Math. Soc., 357, pp.1753~1778 (2004)
- W. X. Ma, "Rational solutions of the Toda lattice equation in Casoratian form", Chaos, Solitons & Fractals, 22, pp.395~406 (2004)
- S. T. Mohyud-Din, "Homotopy perturbation method for solving partial differential equations", 64a, pp.157~170 (2009)
- S. T. Mohyud-Din, "On the coupling of polynomials with correction functional", Int. J. Mod. Phys. B (2009)
- S. T. Mohyud-Din, "Some relatively new techniques for nonlinear problems", Math. Prob. Eng., 2009, pp.25~ (2009)
- S. T. Mohyud-Din, "Travelling wave solutions of seventh-order generalized KdV equations using He’s polynomials", Int. J. Nonlin. Sci. Num. Sim., 10(2), pp.223~229 (2009)
- S. T. Mohyud-Din, "Modified variation of parameters method for solving partial differential equations", Int. J. Mod. Phys. B (2009)
- S. T. Mohyud-Din, "Modified variation of parameters method for differential equations", Wd. Appl. Sci. J., 6(10), pp.1372~1376 (2009)
- S. T. Mohyud-Din, "Modified variation of parameter technique for Thomas-Fermi and fourth-order singular parabolic equations", Int. J. Mod. Phys. B (2009)
- S. T. Mohyud-Din, "Ma’s variation of parameters method for Burger’s and telegraph equations", Int. J. Mod. Phys. B (2009)
- S. T. Mohyud-Din, "Modified variation of parameters method for second-order integro-differential equations and coupled systems", Wd. Appl. Sci. J., 6(9), pp.1298~1303 (2009)
- M. A. Noor, "Homotopy perturbation method for solving sixthorder boundary value problems", Comput. Math. Appl., 55(12), pp.2953~2972 (2008)
- M. A. Noor, "Variational iteration method for solving higher-order nonlinear boundary value problems using He’s polynomials", Int. J. Nonlin. Sci. Num. Simul., 9(2), pp.141~157 (2008)
- M. A. Noor, "Homotopy perturbation method for nonlinear higher-order boundary value problems", Int. J. Nonlin. Sci. Num. Simul., 9(4), pp.395~408 (2008)
- M. A. Noor, "Variation of parameters method for solving fifth-order boundary value problems", Appl. Math. Inf. Sci., 2, pp.135~141 (2008)
- J. I. Ramos, "On the variational iteration method and other iterative techniques for nonlinear differential equations", Appl. Math. Comput., 199(1), pp.39~69 (2008)
- S. S. Siddiqi, "Spline solutions of linear sixth-order boundary value problems", Int. J. Comput. Math., 60, pp.295~304 (1996)
- J. Toomore, "Stellar convection theory II: singlemode study of the secong convection zone in A-type stars", Astrophs. J., 207, pp.545~563 (1976)
- E. H. Twizell, "Numerical methods for sixth-order boundary value problems, in: numerical Mathematics, Singapore, International Series of Numerical Mathematics", pp.495~506 (1988), Birkhauser
- E. H. Twizell, "Numerical methods for the solution of special and general sixth-order boundary value problems, with applications to Benard layer Eigen value problem", Proc. Roy. Soc. Lond. A, 431, pp.433~450 (1990)
- A. M. Wazwaz, "The numerical solution of sixth order boundary value problems by the modified decomposition method", Appl. Math. Comput., 118, pp.311~325 (2001)