×

zbMATH — the first resource for mathematics

The numerical solution of sixth-order boundary value problems by the modified decomposition method. (English) Zbl 1023.65074
Summary: A fast and accurate algorithm is developed for the solution of sixth-order boundary value problems with two-point boundary conditions. A modified form of the Adomian decomposition method is applied to construct the numerical solution for such problems. The scheme is tested on one linear and two nonlinear problems. The results demonstrate reliability and efficiency of the algorithm developed.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Toomore, J.; Zahn, J.R.; Latour, J.; Spiegel, E.A., Stellar convection theory II: single-mode study of the second convection zone in A-type stars, Astrophys. J., 207, 545-563, (1976)
[2] Boutayeb, A.; Twizell, E.H., Numerical methods for the solution of special sixth-order boundary value problems, Int. J. comput. math., 45, 207-233, (1992) · Zbl 0773.65055
[3] Twizell, E.H.; Boutayeb, A., Numerical methods for the solution of special and general sixth-order boundary value problems, with applications to Bénard layer eigenvalue problems, Proc. roy. soc. lond. A, 431, 433-450, (1990) · Zbl 0722.65042
[4] Glatzmaier, G.A., Numerical simulations of stellar convection dynamics at the base of the convection zone, Geophys. fluid dynamics, 31, 137-150, (1985)
[5] Siddiqi, S.S.; Twizell, E.H., Spline solutions of linear sixth-order boundary value problems, Int. J. comput. math., 60, 295-304, (1996) · Zbl 1001.65523
[6] Baldwin, P., 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, 281-305, (1987) · Zbl 0625.76043
[7] Baldwin, P., A localized instability in a Bénard layer, Applicable anal., 24, 117-156, (1987) · Zbl 0588.76076
[8] Chandrasekhar, S., Hydrodynamics and hydromagnetic stability, (1981), Dover New York
[9] Agarwal, R.P., Boundary value problems for high ordinary differential equations, (1986), World Scientific Singapore · Zbl 0598.65062
[10] Chawla, M.M.; Katti, C.P., Finite difference methods for two-point boundary value problems involving higher order differential equations, Bit, 19, 27-33, (1979) · Zbl 0401.65053
[11] E.H. Twizell, Numerical methods for sixth-order boundary value problems, in: Numerical Mathematics, Singapore, 1988, International Series of Numerical Mathematics, vol. 86, Birkhäuser, Basel, 1988, pp. 495-506
[12] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Boston · Zbl 0802.65122
[13] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl., 135, 501-544, (1988) · Zbl 0671.34053
[14] Wazwaz, A.M., A first course in integral equations, (1997), World Scientific River Edge, NJ
[15] Wazwaz, A.M., Analytical approximations and pade approximants for Volterra’s population model, Appl. math. comput., 100, 13-25, (1999) · Zbl 0953.92026
[16] Wazwaz, A.M., A reliable modification of Adomian’s decomposition method, Appl. math. comput., 102, 77-86, (1999) · Zbl 0928.65083
[17] Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comput., 111, 33-51, (2000)
[18] Cherrauault, Y.; Saccomandi, G.; Some, B., New results for convergence of Adomian’s method applied to integral equations, Math. comput. modelling, 16, 2, 85-93, (1992) · Zbl 0756.65083
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.