Analytic solution of singular Emden-Fowler-type equations by Green’s function and homotopy analysis method

Abstract.We propose an iterative scheme for the approximate solution of strongly Emden-Fowler-type equations with Dirichlet-Robin and Neumann-Robin boundary conditions, which model many phenomena in mathematical physics and astrophysics. The present approach is based on Green’s function and a modification of the homotopy analysis method (HAM). Our strategy depends on constructing Green’s function before establishing the recursive scheme for the series solution. In contrast to HAM (M. Danish et al., Comput. Chem. Eng. 36, 57 (2012)), the proposed method avoids solving a sequence of transcendental equations for the undetermined coefficients. Unlike, Adomian decomposition method (ADM) (R. Singh, J. Kumar, Comput. Phys. Commun. 185, 1282 (2014)), the present technique contains an adjustable parameter c0 to control the convergence of the series solution. This convergence control parameter c0 involved in approximations is determined by minimizing the discrete averaged residual error. We find the estimates to resolution in the form of series. Convergence and error analysis of the current method is provided. Several examples of singular boundary value problems are considered to demonstrate the accuracy of the current algorithm. Computational results reveal that the present approach produces better results as compared to some existing iterative methods.

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