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Variational approach to the Lane--Emden equation. (English) Zbl 1022.65076
Summary: By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

65L05Initial value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34A34Nonlinear ODE and systems, general
Full Text: DOI
[1] Wazwaz, A. M.: A new algorithm for solving differential equations of Lane--Emden type. Appl. math. Comput. 118, 287-310 (2001) · Zbl 1023.65067
[2] Bender, C. M.; Pinsky, K. S.; Simmons, L. M.: A new perturbative approach to nonlinear problems. J. math. Phys. 30, No. 7, 1447-1455 (1989) · Zbl 0684.34008
[3] Andrianov, I.; Awrejcewicz, J.: Construction of periodic solution to partial differential equations with nonlinear boundary conditions. Int. J. Nonlin. sci. Numer. simul. 1, No. 4, 327-332 (2000) · Zbl 0977.35031
[4] 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, No. 1, 17-24 (2000) · Zbl 0966.65058
[5] 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, No. 1, 23-28 (1997)