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Variational approach to the sixth-order boundary value problems. (English) Zbl 1025.65043
Summary: Recently, A.-M. Wazwaz [Appl. Math. Comput. 118, 311-325 (2001; Zbl 1023.65074)] applied the Adomian’s decomposition method to solve analytically the solution of sixth-order boundary value problems. The same problem is discussed via the variational principle, which reveals to be much more simpler and much more efficient.

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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[1] Wazwaz, A.M., The numerical solution of sixth-order boundary value problems by the modified decomposition method, Appl. math. comput., 118, 311-325, (2001) · Zbl 1023.65074
[2] Wazwaz, A.M., The modified Adomian decomposition method for solving linear and nonlinear boundary value problems of 10th-order and 12th-order, Int. J. nonlin. sci. numer. simul., 1, 1, 17-24, (2000) · Zbl 0966.65058
[3] He, J.H., Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics, Int. J. turbo & jet-engines, 14, 1, 23-28, (1997)
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