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An algorithm based on the variational iteration technique for the Bratu-type and the Lane–Emden problems

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Abstract

In this paper, a new algorithm for the numerical solution of the Bratu-type and the Lane–Emden problems with boundary conditions is presented. The proposed algorithm is based on the variational iteration method (VIM), where all the boundary conditions are used before designing the recursive scheme for the approximate solutions of considered boundary value problems. Unlike the VIM, the proposed algorithm avoids solving a sequence of nonlinear algebraic or (transcendental) equations for the undetermined coefficients. Convergence and error analysis of the proposed method is also given. Illustrative examples, of two different models, are examined to demonstrate the accuracy, applicability, and generality of the proposed method.

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Correspondence to Randhir Singh.

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Das, N., Singh, R., Wazwaz, AM. et al. An algorithm based on the variational iteration technique for the Bratu-type and the Lane–Emden problems. J Math Chem 54, 527–551 (2016). https://doi.org/10.1007/s10910-015-0575-6

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  • DOI: https://doi.org/10.1007/s10910-015-0575-6

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