An efficient numerical technique for the solution of nonlinear singular boundary value problems
In this work, a new technique based on Greens function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Greens function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
nonlinear singular boundary value problem greens function adomian decomposition method modified adomian decomposition method series solutions emdenfowler equation