Applied Mathematics & Information Sciences

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We propose a new modification to Adomian decomposition method for numerical treatment of the time-dependent Emden- Fowler-types equations with the Neumann and Dirichlet boundary conditions. In new modified method, we use all the boundary conditions to derive an integral equation before establishing the recursive scheme. The new modified decomposition method (MDM) will be used without unknown constants while computing the successive solution components. Unlike the recursive schemes that result from using the ADM, the new MDM avoids solving a sequence of nonlinear algebraic or transcendental equations for the derivation of unknown constants. Moreover, the proposed technique is reliable enough to overcome the difficulty of the singular point at x = 0. Five illustrative examples are examined to demonstrate the accuracy and applicability of the proposed method.

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