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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. [ABSTRACT FROM AUTHOR]

In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order Bratu's differential equation. Convergence analysis of presented method is discussed. The numerical approximations to the exact solution are computed and compared with other existing methods. Our presented method produces more accurate results in comparison with those obtained by Adomian decomposition, Laplace decomposition, B-spline, non-polynomial spline and Lie-group shooting methods. Our yardstick is absolute error. The comparison of the results with exact ones is made to confirm the validity and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur. [ABSTRACT FROM AUTHOR]